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Quadratic Equation Questions for DU JAT and IPMAT

Author : Palak Khanna

September 7, 2022

SHARE

In most of the entrance exams, you will have a mathematics section that includes questions from various concepts and the quadratic equation is one of the essential topics in the Mathematics subject.

It might look complex, but you can solve them in no time if you apply the correct formulas and the right methods.

This post will take you through the essential questions for DU JAT and  IPMAT entrance exams. 

Several examples of important questions, solutions, and practice papers are offered in the blog. 

What are Quadratic Equations?

Quadratic equations are a type of equation in algebra that can be rearranged in standard form as ax^{2}+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers, and a ≠ 0.

If a = 0, the equation is linear, not quadratic, as there is no ax^2 term.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

  • 6x² + 11x - 35 = 0.
  • x² -x - 3 = 0.
  • 2x² - 4x - 2 = 0.
  • -4x² - 7x +12 = 0.
  • 5x² - 2x - 9 = 0.
  • 20x² -15x - 10 = 0.

Download Free Study Material for IPMAT and DU JAT Exams by SuperGrads

How to Solve DU JAT Quadratic Equation Questions?

You can solve below questions using various methods; one such is by factorization. 

  1. Firstly, you need to put all the terms on one side of the equal sign, leaving zero on the other side. 
  2. Do the factorization.
  3. Set each factor equal to zero.
  4. Solve each of these equations.
  5. Check your solution by inserting your answer into the original equation.

ipmat mock test

ipmat Mock test

DU JAT Quadratic Equation Questions and Answers PDF

For more questions, download the pdf below, which includes questions and solutions. Enhance your preparation for DU JAT by solving these questions and score good marks in the mathematics section.

Download Quadratic Equation Questions PDF

Important Formulas to Solve Quadratic Equation Questions for DU JAT and IPMAT

Here is the list of formulas that you can use to solve DU JAT Questions. 

  • The standard form of a quadratic equation is ax2 + bx + c = 0
  • The discriminant of the quadratic equation is D = b- 4ac
  • For D > 0 the roots are real and distinct.
  • For D = 0 the roots are real and equal.
  • For D < 0 the roots do not exist, or the roots are imaginary.
  • The formula to find the roots of the quadratic equation is x = 
  • The sum of the roots of a quadratic equation is α + β = -b/a = - Coefficient of x/ Coefficient of x2.
  • The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x2
  • The quadratic equation having roots α, β, is x2 - (α + β)x + αβ = 0.
  • For positive values of a (a > 0), the quadratic expression f(x) = ax+ bx + c has a minimum value at x = -b/2a.
  • For negative value of a (a < 0), the quadratic expression f(x) = ax+ bx + c has a maximum value at x = -b/2a.
  • For a > 0, the range of the quadratic equation ax2 + bx + c = 0 is [b2 - 4ac/4a, ∞)
  • For a < 0, the range of the quadratic equation ax2 + bx + c = 0 is : (∞, -(b2 - 4ac)/4a]

Important Quadratic Equation Questions and Answers for DU JAT and IPMAT

Here is the list of questions curated from previous year's DU JAT Question Papers. The subject mentor from Supergrads has solved the questions below with a detailed explanation. 

Solve these quadratic equations and enhance your preparation for the upcoming DU JAT exam.

1. If 𝛼 ≠ 𝛽 but α 2 = 5α − 3 and β 2 = 5β − 3 then the equation whose roots are 𝛼/𝛽 and 𝛽/𝛼 is

  • (a) 3x 2 − 25x +3 = 0
  • (b) x 2 + 5π‘₯ −3 = 0
  • (c) x 2 − 5π‘₯ +3 = 0
  • (d) 3π‘₯ 2 − 19π‘₯ + 3 = 0

2. Difference between the corresponding roots of x 2 + ax+ b = 0 and x 2 + bx + π‘Ž = 0 is same and π‘Ž ≠ 𝑏, then

  • (a) π‘Ž + 𝑏 + 4 = 0
  • (b) π‘Ž + 𝑏 − 4 = 0
  • (c) π‘Ž − 𝑏 − 4 = 0
  • (d) π‘Ž − 𝑏 + 4 = 0

3. If p and q are the roots of the equation x2 + px + q = 0 then

  • (a) 𝑝 = 1, π‘ž = −2
  • (b) 𝑝 = 0, π‘ž = 1
  • (c) 𝑝 = −2, π‘ž = 0
  • (d) 𝑝 = −2, π‘ž = 1

4. If a , b , c are distinct positive real numbers and a2 + b 2 + c 2 = 1 then π‘Žπ‘ + 𝑏𝑐 + π‘π‘Ž is

  • (a) less than 1
  • (b) equal to 1
  • (c) greater than 1
  • (d) any real no

5. The value of a for which one root of the quadratic equation (a2 2 − 5a+ 3)x 22 + (3a − 1)x + 2 = 0 is twice as large as the other is

  • (a) -2/3
  • (b) 1/3
  • (c) -1/3
  • (d) 2/3

6. If the sum of the roots of the quadratic equation ax2 +bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in 

  • (a) geometric progression
  • (b) harmonic progression
  • (c) arithmetic-geometric progression
  • (d) arithmetic progression

7. Let two numbers have an arithmetic mean nine and geometric mean 4 . Then these numbers are the roots of the quadratic equation

  • (a) x 2 + 18π‘₯ −16 = 0
  • (b) x 2 − 18π‘₯ +16 = 0
  • (c) x 2 + 18π‘₯ +16 = 0
  • (d) x 2 − 18π‘₯ −16 = 0

8. If (1 −𝑝) is a root of quadratic equation x2 + 𝑝π‘₯ +(1 −𝑝) = 0 then its roots are

  • (a) 0, -1
  • (b) -1, 1
  • (c) 0, 1
  • (d) -1, 2

9. If one root of the equation x2+ 𝑝π‘₯ + 12 = 0 is 4 while the equation x 2 + 𝑝π‘₯ + π‘ž = 0 has equal roots, then the value of q is

  • (a) 3
  • (b) 12
  • (c) 49/4
  • (d) 4

10.  If the roots of the equation x2 −𝑏π‘₯ + 𝑐 = 0 be two consecutive integers, then b 2 −4𝑐 equals

  • (a) 3
  • (b) -2
  • (c) 1
  • (d) 2

Frequently Asked Questions

There are various advantages of solving IPMAT Previous Year papers such as-

You will know which of the topics are most important and can prepare accordingly. You will get to understand the question pattern which will help you prepare in the correct manner. Solving IPMAT Previous year papers in a time-bound exam like environment will remove your exam fear and nervousness on the day of the real exam. It will increase your speed and accuracy on the day of the actual exam.

No. You can take DU JAT Mock Tests whenever your time permits.
With the right method of preparation, the DU JAT Exam can be easily cleared. Aspirants must prepare for each subject in a better way to score more marks.
The best books for DU JAT Exam preparation are as follows-
  • The Perfect Study Resource for - Delhi University (DU) BMS Entrance Test
  • University of Delhi BMS/BBA (FIA)/B.A. Business Economics Joint Admission Test Guide: BMS (Bachelor of Management Studies) Common Entrance Test Guide (Hons.)
  • A Complete Self Study Guide BBA/BBS/BBM (Bachelor of Business Administration/Studies/Management) Entrance Examinations 2017 (Old Edition)
  • BBA: Entrance Examination - 16 Practice Sets for BBA - BBS,SET (General)
  • Edge Advantage Series - BBA 10 Practice Sets
Yes. We will provide subject-wise DU JAT Mock Tests after completion of each subject.
Arun Sharma's quantitative aptitude books is good for IPMAT exam. However, the level of difficulty is a bit higher.
  • Home
  • Quadratic Equation Q...

Quadratic Equation Questions for DU JAT and IPMAT

Author : Palak Khanna

Updated On : September 7, 2022

SHARE

In most of the entrance exams, you will have a mathematics section that includes questions from various concepts and the quadratic equation is one of the essential topics in the Mathematics subject.

It might look complex, but you can solve them in no time if you apply the correct formulas and the right methods.

This post will take you through the essential questions for DU JAT and  IPMAT entrance exams. 

Several examples of important questions, solutions, and practice papers are offered in the blog. 

What are Quadratic Equations?

Quadratic equations are a type of equation in algebra that can be rearranged in standard form as ax^{2}+bx+c=0 where x represents an unknown, and a, b, and c represent known numbers, and a ≠ 0.

If a = 0, the equation is linear, not quadratic, as there is no ax^2 term.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

  • 6x² + 11x - 35 = 0.
  • x² -x - 3 = 0.
  • 2x² - 4x - 2 = 0.
  • -4x² - 7x +12 = 0.
  • 5x² - 2x - 9 = 0.
  • 20x² -15x - 10 = 0.

Download Free Study Material for IPMAT and DU JAT Exams by SuperGrads

How to Solve DU JAT Quadratic Equation Questions?

You can solve below questions using various methods; one such is by factorization. 

  1. Firstly, you need to put all the terms on one side of the equal sign, leaving zero on the other side. 
  2. Do the factorization.
  3. Set each factor equal to zero.
  4. Solve each of these equations.
  5. Check your solution by inserting your answer into the original equation.

ipmat mock test

ipmat Mock test

DU JAT Quadratic Equation Questions and Answers PDF

For more questions, download the pdf below, which includes questions and solutions. Enhance your preparation for DU JAT by solving these questions and score good marks in the mathematics section.

Download Quadratic Equation Questions PDF

Important Formulas to Solve Quadratic Equation Questions for DU JAT and IPMAT

Here is the list of formulas that you can use to solve DU JAT Questions. 

  • The standard form of a quadratic equation is ax2 + bx + c = 0
  • The discriminant of the quadratic equation is D = b- 4ac
  • For D > 0 the roots are real and distinct.
  • For D = 0 the roots are real and equal.
  • For D < 0 the roots do not exist, or the roots are imaginary.
  • The formula to find the roots of the quadratic equation is x = 
  • The sum of the roots of a quadratic equation is α + β = -b/a = - Coefficient of x/ Coefficient of x2.
  • The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x2
  • The quadratic equation having roots α, β, is x2 - (α + β)x + αβ = 0.
  • For positive values of a (a > 0), the quadratic expression f(x) = ax+ bx + c has a minimum value at x = -b/2a.
  • For negative value of a (a < 0), the quadratic expression f(x) = ax+ bx + c has a maximum value at x = -b/2a.
  • For a > 0, the range of the quadratic equation ax2 + bx + c = 0 is [b2 - 4ac/4a, ∞)
  • For a < 0, the range of the quadratic equation ax2 + bx + c = 0 is : (∞, -(b2 - 4ac)/4a]

Important Quadratic Equation Questions and Answers for DU JAT and IPMAT

Here is the list of questions curated from previous year's DU JAT Question Papers. The subject mentor from Supergrads has solved the questions below with a detailed explanation. 

Solve these quadratic equations and enhance your preparation for the upcoming DU JAT exam.

1. If 𝛼 ≠ 𝛽 but α 2 = 5α − 3 and β 2 = 5β − 3 then the equation whose roots are 𝛼/𝛽 and 𝛽/𝛼 is

  • (a) 3x 2 − 25x +3 = 0
  • (b) x 2 + 5π‘₯ −3 = 0
  • (c) x 2 − 5π‘₯ +3 = 0
  • (d) 3π‘₯ 2 − 19π‘₯ + 3 = 0

2. Difference between the corresponding roots of x 2 + ax+ b = 0 and x 2 + bx + π‘Ž = 0 is same and π‘Ž ≠ 𝑏, then

  • (a) π‘Ž + 𝑏 + 4 = 0
  • (b) π‘Ž + 𝑏 − 4 = 0
  • (c) π‘Ž − 𝑏 − 4 = 0
  • (d) π‘Ž − 𝑏 + 4 = 0

3. If p and q are the roots of the equation x2 + px + q = 0 then

  • (a) 𝑝 = 1, π‘ž = −2
  • (b) 𝑝 = 0, π‘ž = 1
  • (c) 𝑝 = −2, π‘ž = 0
  • (d) 𝑝 = −2, π‘ž = 1

4. If a , b , c are distinct positive real numbers and a2 + b 2 + c 2 = 1 then π‘Žπ‘ + 𝑏𝑐 + π‘π‘Ž is

  • (a) less than 1
  • (b) equal to 1
  • (c) greater than 1
  • (d) any real no

5. The value of a for which one root of the quadratic equation (a2 2 − 5a+ 3)x 22 + (3a − 1)x + 2 = 0 is twice as large as the other is

  • (a) -2/3
  • (b) 1/3
  • (c) -1/3
  • (d) 2/3

6. If the sum of the roots of the quadratic equation ax2 +bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in 

  • (a) geometric progression
  • (b) harmonic progression
  • (c) arithmetic-geometric progression
  • (d) arithmetic progression

7. Let two numbers have an arithmetic mean nine and geometric mean 4 . Then these numbers are the roots of the quadratic equation

  • (a) x 2 + 18π‘₯ −16 = 0
  • (b) x 2 − 18π‘₯ +16 = 0
  • (c) x 2 + 18π‘₯ +16 = 0
  • (d) x 2 − 18π‘₯ −16 = 0

8. If (1 −𝑝) is a root of quadratic equation x2 + 𝑝π‘₯ +(1 −𝑝) = 0 then its roots are

  • (a) 0, -1
  • (b) -1, 1
  • (c) 0, 1
  • (d) -1, 2

9. If one root of the equation x2+ 𝑝π‘₯ + 12 = 0 is 4 while the equation x 2 + 𝑝π‘₯ + π‘ž = 0 has equal roots, then the value of q is

  • (a) 3
  • (b) 12
  • (c) 49/4
  • (d) 4

10.  If the roots of the equation x2 −𝑏π‘₯ + 𝑐 = 0 be two consecutive integers, then b 2 −4𝑐 equals

  • (a) 3
  • (b) -2
  • (c) 1
  • (d) 2

Frequently Asked Questions

There are various advantages of solving IPMAT Previous Year papers such as-

You will know which of the topics are most important and can prepare accordingly. You will get to understand the question pattern which will help you prepare in the correct manner. Solving IPMAT Previous year papers in a time-bound exam like environment will remove your exam fear and nervousness on the day of the real exam. It will increase your speed and accuracy on the day of the actual exam.

No. You can take DU JAT Mock Tests whenever your time permits.
With the right method of preparation, the DU JAT Exam can be easily cleared. Aspirants must prepare for each subject in a better way to score more marks.
The best books for DU JAT Exam preparation are as follows-
  • The Perfect Study Resource for - Delhi University (DU) BMS Entrance Test
  • University of Delhi BMS/BBA (FIA)/B.A. Business Economics Joint Admission Test Guide: BMS (Bachelor of Management Studies) Common Entrance Test Guide (Hons.)
  • A Complete Self Study Guide BBA/BBS/BBM (Bachelor of Business Administration/Studies/Management) Entrance Examinations 2017 (Old Edition)
  • BBA: Entrance Examination - 16 Practice Sets for BBA - BBS,SET (General)
  • Edge Advantage Series - BBA 10 Practice Sets
Yes. We will provide subject-wise DU JAT Mock Tests after completion of each subject.
Arun Sharma's quantitative aptitude books is good for IPMAT exam. However, the level of difficulty is a bit higher.

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