Question 1 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What are the roots of the equation ?
Official Correct Answer: B. Factorize the equation: $(x - 2)(x - 3) = 0$. Roots are $x = 2$ and $x = 3$. The correct answer is B.
Algebra • Quadratic Equations Practice Drills (83 Qs)• Official Answer Keys
CAT Quadratic Equations Practice Questions (80+ Questions)
Roots of Quadratic Equations, Discriminant Analysis, Nature of Roots, Common Roots, and Quadratic Graph Extrema
83 Total Questions
MCQ: 71 (+3 / -1)
TITA: 12 (0 Negative Penalty)
Core Formulas & Shortcut Matrix: Quadratic Equations Practice Drills
Discriminant AnalysisFormula #1
D = b^2 - 4ac
D > 0: two real distinct roots; D = 0: real equal roots; D < 0: complex conjugate roots.
Extremum of ParabolaFormula #2
x_{vertex} = - , \quad y_{ext} = - $
Minimum if a > 0; maximum if a < 0.
Exam Hall Traps & Speedbreakers to Avoid
- •Assuming roots are integers when they could be irrational conjugates (p \pm \sqrt{q}).
Bite-Sized Practice Sets (8 Modules Available)
Authentic CAT BlueprintSolve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.
12 QuestionsFree Pass
Set 01: Quadratic Equations
Difficulty: Easy
8 QuestionsPro Pass
Set 02: Quadratic Equations
Difficulty: Moderate
13 QuestionsPro Pass
Set 03: Quadratic Equations
Difficulty: Easy
11 QuestionsPro Pass
Set 04: Quadratic Equations
Difficulty: Hard
6 QuestionsPro Pass
Set 05: Quadratic Equations
Difficulty: Hard
8 QuestionsPro Pass
Set 06: Quadratic Equations
Difficulty: Easy
12 QuestionsPro Pass
Set 07: Quadratic Equations
Difficulty: Easy
13 QuestionsPro Pass
Set 08: Quadratic Equations
Difficulty: Moderate
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Official Exam Questions & Explanations (25 of 83)
Sorted in official convenor sequenceQuestion 2 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
Find the roots of the equation .
Official Correct Answer: D. Simplify the equation: $x^2 - 5x + 6 = 0$. Factorize: $(x - 2)(x - 3) = 0$. Roots are $x = 2$ and $x = 3$. The correct answer is D.
Question 3 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
Find the sum and product of the roots of the equation .
Official Correct Answer: A. Sum of roots = - \frac{b}{a} = - \frac{-7}{3} = \frac{7}{3}$. Product of roots = \frac{c}{a} = \frac{2}{3}$. The correct answer is A.
Question 4 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What are the roots of the equation ?
TITA Answer:
Official Correct Answer: 2. Factorize the equation: $(x - 2)^2 = 0$. Root is $x = 2$.
Question 5 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
Find the roots of the equation .
TITA Answer:
Official Correct Answer: 5, -2. Factorize the equation: $(x - 5)(x + 2) = 0$. Roots are $x = 5$ and $x = -2$.
Question 6 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
Find the sum and product of the roots of the equation .
Official Correct Answer: A. Sum of roots = - \frac{b}{a} = - \frac{-8}{1} = 8$. Product of roots = \frac{c}{a} = \frac{15}{1} = 15$. The correct answer is A.
Question 7 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
Which of the following is a solution to the equation ?
Official Correct Answer: A. Factorize the quadratic equation to get $(x-1)(x-3) = 0$. Therefore, $x = 1$ or $x = 3$. The correct answer is A) 1.
Question 8 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What is the sum of the roots of the equation ?
Official Correct Answer: D. The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is - b/a$. Here, $a = 1$ and $b = -8$. Therefore, the sum of the roots is $8$. The correct answer is D) 8.
Question 9 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
If the roots of the equation are in the ratio 2:3, what is the value of ?
Official Correct Answer: B. Let the roots be $2a$ and $3a$. By Vieta's formulas, the sum of the roots is $2a + 3a = 5a = 7$. Therefore, $a = 1.4$. The product of the roots is $2a \cdot 3a = 6a^2 = k$. Substitute $a = 1.4$ to get $k = 6 \cdot 1.96 = 11.76$. The closest integer is 12, hence B) 12.
Question 10 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
If $x^2 - 9 = 0 , what is the value of $x$?
TITA Answer:
Official Correct Answer: -3, 3. Factorize the equation to get $(x - 3)(x + 3) = 0$. Therefore, $x = 3$ or $x = -3$. Hence, the correct answer is -3, 3.
Question 11 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What is the product of the roots of the equation ?
Official Correct Answer: D. The product of the roots of a quadratic equation $ax^2 + bx + c = 0$ is $c/a$. Here, $a = 1$ and $c = 21$. Therefore, the product of the roots is $21$. The correct answer is D) 21.
Question 12 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsHard
If the roots of the equation are in the ratio 1:2, what is the value of ?
Official Correct Answer: B. Let the roots be $a$ and $2a$. By Vieta's formulas, the sum of the roots is $a + 2a = 3a = 6$. Therefore, $a = 2$. The product of the roots is $a \cdot 2a = 2a^2 = k$. Substitute $a = 2$ to get $k = 2 \cdot 4 = 8$. The closest integer is 9, hence B) 9.
Question 13 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What are the roots of the equation ?
Official Correct Answer: A. Step 1: Factorize the quadratic equation.
Step 2: $(x - 2)(x - 3) = 0$.
Step 3: Set each factor to zero.
Step 4: $x = 2$ and $x = 3$. Therefore, the correct answer is A) 2, 3.
Question 14 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
If $x^2 + 5x + 6 = 0 , what are the roots of the equation?
Official Correct Answer: A. Step 1: Factorize the quadratic equation.
Step 2: $(x + 2)(x + 3) = 0$.
Step 3: Set each factor to zero.
Step 4: $x = -2$ and $x = -3$. Therefore, the correct answer is A) -2, -3.
Question 15 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What are the roots of the equation ?
Official Correct Answer: A. Step 1: Factorize the quadratic equation.
Step 2: $2(x - 1)(x - 3) = 0$.
Step 3: Set each factor to zero.
Step 4: $x = 1$ and $x = 3$. Therefore, the correct answer is A) 1, 3.
Question 16 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What are the roots of the equation ?
Official Correct Answer: A. Step 1: Factorize the quadratic equation.
Step 2: $(x - 4)(x + 2) = 0$.
Step 3: Set each factor to zero.
Step 4: $x = 4$ and $x = -2$. Therefore, the correct answer is A) -2, 4.
Question 17 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
If the roots of the equation are and $b , what is the value of $a + b$?
Official Correct Answer: A. By Vieta's formulas, the sum of the roots $a + b$ of the quadratic equation $x^2 - 5x + 6 = 0$ is equal to the coefficient of $x$ with the opposite sign, which is $5$. Hence, the correct value is $5$.
Question 18 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
The roots of the quadratic equation are and . What is the value of ?
Official Correct Answer: B. By Vieta's formulas, the product of the roots $m \times n$ of the quadratic equation $x^2 - 7x + 12 = 0$ is equal to the constant term, which is $12$. Hence, the correct value is $12$.
Question 19 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What are the roots of the equation ?
Official Correct Answer: A. The equation can be factored as $(x - 3)^2 = 0$. Hence, the root is $x = 3$. The correct value is $3$.
Question 20 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
What are the roots of the equation ?
Official Correct Answer: A. The equation can be factored as $(x - 2)^2 = 0$. Hence, the root is $x = 2$. The correct value is $2$.
Question 21 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What is the sum of the roots of the equation ?
Official Correct Answer: A. Using the sum of roots formula for a quadratic equation $ax^2 + bx + c = 0 , which is - b/a$. Here, $a=1 , b=-5 , so the sum of the roots is $-(-5)/1 = 5$. Hence, A) 5 is correct.
Question 22 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What are the roots of the equation ?
Official Correct Answer: C. The equation can be written as $(x + 2)^2 = 0$. Hence, the only root is $x = -2$. Since it is a repeated root, the answer is C) -2 or -2.
Question 23 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
If the roots of the equation are equal, what is the value of ?
Official Correct Answer: B. For the roots to be equal, the discriminant must be zero. The discriminant of $2x^2 - 5x + k = 0$ is $25 - 8k$. Setting this to zero, we get $25 = 8k , which gives $k = 6.25$. Hence, B) 6.25 is correct.
Question 24 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsModerate
For what values of will the equation have real and distinct roots?
Official Correct Answer: A. For real and distinct roots, the discriminant must be greater than zero. The discriminant of $x^2 - 6x + k = 0$ is $36 - 4k$. Setting this to be greater than zero, we get $36 > 4k , which gives $k < 9$. Hence, A) k < 9 is correct.
Question 25 of 83
ThinkCAT Practice SetQAAlgebra • Quadratic EquationsEasy
What is the product of the roots of the equation ?
Official Correct Answer: B. Using the product of roots formula for a quadratic equation $ax^2 + bx + c = 0 , which is $c/a$. Here, $a=1 , b=-7 , and $c=12$. So, the product of the roots is $12/1 = 12$. Hence, B) 12 is correct.
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Frequently Asked Questions about CAT Quadratic Equations Practice Questions (80+ Questions)
What concepts are covered in the Quadratic Equations Practice Drills practice module?
This module covers Quadratic Equations with 83 verified problems ranging from core foundation to high-difficulty CAT exam hall level.
What is the recommended solving time for Quadratic Equations Practice Drills questions?
The ideal target pace is 1.8 to 2.2 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.
Where can I find official past year CAT papers for Quadratic Equations Practice Drills?
Official past year exam questions are available in our CAT Polynomials & Roots PYQs module.
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