Updated On : May 14, 2024

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.

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.

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

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

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.

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

- The standard form of a quadratic equation is ax
^{2}+ bx + c = 0 - The discriminant of the quadratic equation is D = b
^{2 }- 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 x
^{2}. - The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x
^{2} - The quadratic equation having roots α, β, is x
^{2}- (α + β)x + αβ = 0. - For positive values of a (a > 0), the quadratic expression f(x) = ax
^{2 }+ bx + c has a minimum value at x = -b/2a. - For negative value of a (a < 0), the quadratic expression f(x) = ax
^{2 }+ bx + c has a maximum value at x = -b/2a. - For a > 0, the range of the quadratic equation ax
^{2}+ bx + c = 0 is [b^{2}- 4ac/4a, ∞) - For a < 0, the range of the quadratic equation ax
^{2}+ bx + c = 0 is : (∞, -(b^{2}- 4ac)/4a]

Download Quadratic Equation Questions PDF

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}+ 5𝑥 −3 = 0 - (c) x
^{2}− 5𝑥 +3 = 0 - (d)
**3𝑥**^{2}− 19𝑥 + 3 = 0

2. Difference between the corresponding roots of x ^{2} + ax+ b = 0 and x ^{2} + bx + 𝑎 = 0 is same and 𝑎 ≠ 𝑏, then

**(a) 𝑎 + 𝑏 + 4 = 0**- (b) 𝑎 + 𝑏 − 4 = 0
- (c) 𝑎 − 𝑏 − 4 = 0
- (d) 𝑎 − 𝑏 + 4 = 0

3. If p and q are the roots of the equation x^{2} + px + q = 0 then

**(a) 𝑝 = 1, 𝑞 = −2**- (b) 𝑝 = 0, 𝑞 = 1
- (c) 𝑝 = −2, 𝑞 = 0
- (d) 𝑝 = −2, 𝑞 = 1

4. If a , b , c are distinct positive real numbers and a^{2} + b ^{2} + c ^{2} = 1 then 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 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 (a^{2} 2 − 5a+ 3)x ^{2}2 + (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 ax^{2} +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}+ 18𝑥 −16 = 0 **(b) x**^{2}− 18𝑥 +16 = 0- (c) x
^{2}+ 18𝑥 +16 = 0 - (d) x
^{2}− 18𝑥 −16 = 0

8. If (1 −𝑝) is a root of quadratic equation x^{2} + 𝑝𝑥 +(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 x^{2}+ 𝑝𝑥 + 12 = 0 is 4 while the equation x ^{2} + 𝑝𝑥 + 𝑞 = 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 x^{2} −𝑏𝑥 + 𝑐 = 0 be two consecutive integers, then b ^{2} −4𝑐 equals

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

Download Free IPMAT Study Material

Fill your details

Frequently Asked Questions

Why should we solve IPMAT Previous Year Papers?

Is there any fixed time to take DU JAT Mock Tests?

Is DU JAT Exam tough to clear?

Which are the best books for DU JAT Exam preparation?

Will you provide subject-wise DU JAT Mock Tests 2025?

Is Arun Sharma book is good for IPMAT 2025 exam?

May 14, 2024

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.

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.

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

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

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.

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

- The standard form of a quadratic equation is ax
^{2}+ bx + c = 0 - The discriminant of the quadratic equation is D = b
^{2 }- 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 x
^{2}. - The product of the Root of the quadratic equation is αβ = c/a = Constant term/ Coefficient of x
^{2} - The quadratic equation having roots α, β, is x
^{2}- (α + β)x + αβ = 0. - For positive values of a (a > 0), the quadratic expression f(x) = ax
^{2 }+ bx + c has a minimum value at x = -b/2a. - For negative value of a (a < 0), the quadratic expression f(x) = ax
^{2 }+ bx + c has a maximum value at x = -b/2a. - For a > 0, the range of the quadratic equation ax
^{2}+ bx + c = 0 is [b^{2}- 4ac/4a, ∞) - For a < 0, the range of the quadratic equation ax
^{2}+ bx + c = 0 is : (∞, -(b^{2}- 4ac)/4a]

Download Quadratic Equation Questions PDF

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}+ 5𝑥 −3 = 0 - (c) x
^{2}− 5𝑥 +3 = 0 - (d)
**3𝑥**^{2}− 19𝑥 + 3 = 0

2. Difference between the corresponding roots of x ^{2} + ax+ b = 0 and x ^{2} + bx + 𝑎 = 0 is same and 𝑎 ≠ 𝑏, then

**(a) 𝑎 + 𝑏 + 4 = 0**- (b) 𝑎 + 𝑏 − 4 = 0
- (c) 𝑎 − 𝑏 − 4 = 0
- (d) 𝑎 − 𝑏 + 4 = 0

3. If p and q are the roots of the equation x^{2} + px + q = 0 then

**(a) 𝑝 = 1, 𝑞 = −2**- (b) 𝑝 = 0, 𝑞 = 1
- (c) 𝑝 = −2, 𝑞 = 0
- (d) 𝑝 = −2, 𝑞 = 1

4. If a , b , c are distinct positive real numbers and a^{2} + b ^{2} + c ^{2} = 1 then 𝑎𝑏 + 𝑏𝑐 + 𝑐𝑎 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 (a^{2} 2 − 5a+ 3)x ^{2}2 + (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 ax^{2} +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}+ 18𝑥 −16 = 0 **(b) x**^{2}− 18𝑥 +16 = 0- (c) x
^{2}+ 18𝑥 +16 = 0 - (d) x
^{2}− 18𝑥 −16 = 0

8. If (1 −𝑝) is a root of quadratic equation x^{2} + 𝑝𝑥 +(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 x^{2}+ 𝑝𝑥 + 12 = 0 is 4 while the equation x ^{2} + 𝑝𝑥 + 𝑞 = 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 x^{2} −𝑏𝑥 + 𝑐 = 0 be two consecutive integers, then b ^{2} −4𝑐 equals

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

Download Free IPMAT Study Material

Fill your details

Frequently Asked Questions

Why should we solve IPMAT Previous Year Papers?

Is there any fixed time to take DU JAT Mock Tests?

Is DU JAT Exam tough to clear?

Which are the best books for DU JAT Exam preparation?

Will you provide subject-wise DU JAT Mock Tests 2025?

Is Arun Sharma book is good for IPMAT 2025 exam?