The quadratic equation is one of the essential topics in Mathematics subject. In most of the entrance exams, you will have a mathematics section that shall include questions from various concepts. Quadratic Equations might look complex, but you can solve them in no time if you apply the correct formulas.

This post shall take you through the essential quadratic equation questions for DU JAT and other entrance exams. Know the important questions asked and solve them quickly, along with solutions for the practice questions.

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, where 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:

You can solve quadratic equation questions using various methods; one type is by factorisation.

Firstly, you need to put all the terms on one side of the equal sign, leaving zero on the other side.

Do the factorisation.

Set each factor equal to zero.

Solve each of these equations.

Check your solution by inserting your answer into the original equation.

Important Formulas to Solve Quadratic Equation Questions

Here is the list of formulas that you can use to solve DU JAT Quadratic Equation 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]

Important Quadratic Equation Questions and Answers for DU JAT

Here is the list of quadratic equation questions curated from previous year 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

DU JAT Quadratic Equation Questions and Answers PDF

For more questions on quadratic equation 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.