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Quadratic Equations Practice Questions

JEE · Mathematics · 1935 free MCQs with instant results and detailed explanations.

1935
Total
390
Easy
832
Medium
713
Hard

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Topics in Quadratic Equations

Transformation of Equations 375
Common Roots 431
Relation Between Roots and Coefficients 344
Discriminant 342
Nature of Roots 443

Sample Questions from Quadratic Equations

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
For which value of k will the equation x² + 4x + k = 0 have real and equal roots?
A. 4
B. 5
C. 6
D. 8
Show Answer & Explanation
Correct Answer: A
For real and equal roots, D = 0. Here, D = 4² - 4*1*k = 16 - 4k, set D = 0 gives k = 4.
Q2
Easy
What is the nature of roots for the equation 3x² + 2x + 5 = 0?
A. Real and distinct
B. Real and equal
C. Complex
D. Rational
Show Answer & Explanation
Correct Answer: C
D = (2)² - 4*3*5 = 4 - 60 = -56, which is negative indicating complex roots.
Q3
Easy
If the roots of the equation x² - 3x + 2 = 0 are a and b, then what is the value of a + b?
A. 2
B. 3
C. 4
D. 5
Show Answer & Explanation
Correct Answer: B
By Vieta's formulas, a + b = -b/a = 3/1 = 3.
Q4
Medium
If the roots of the quadratic equation ax^2 + bx + c = 0 are real and equal, which of the following must be true regarding the discriminant?
A. b^2 - 4ac = 0
B. b^2 - 4ac > 0
C. b^2 - 4ac < 0
D. b^2 - 4ac = 1
Show Answer & Explanation
Correct Answer: A
For a quadratic equation to have real and equal roots, the discriminant (b^2 - 4ac) must be zero.
Q5
Medium
For the quadratic equation x^2 - 6x + k = 0 to have no real roots, what is the condition on the value of k?
A. k < 9
B. k = 6
C. k > 0
D. k = 0
Show Answer & Explanation
Correct Answer: A
The discriminant must be less than zero (b^2 - 4ac < 0). Here, the condition is -6^2 - 4(1)(k) < 0, leading to k < 9.
Q6
Medium
Consider the quadratic equation 2x^2 + 4x + k = 0. For this equation to have distinct real roots, the value of k must satisfy which of the following inequalities?
A. k < 8
B. k > 8
C. k = 0
D. k = 4
Show Answer & Explanation
Correct Answer: A
To have distinct real roots, the discriminant must be greater than zero. Here, the discriminant is 4^2 - 4(2)(k) > 0, which simplifies to k < 8.
Q7
Medium
For the quadratic equation ax^2 + bx + c = 0, what condition must the discriminant fulfill for the equation to have real and equal roots?
A. b^2 - 4ac = 0
B. b^2 - 4ac > 0
C. b^2 - 4ac < 0
D. b^2 - 4ac = 1
Show Answer & Explanation
Correct Answer: A
The discriminant b^2 - 4ac determines the nature of the roots. For real and equal roots, it must equal zero.
Q8
Hard
If the quadratic equation ax² + bx + c = 0 has real roots, what can be inferred about the discriminant (D)?
A. D > 0
B. D = 0
C. D ≥ 0
D. D < 0
Show Answer & Explanation
Correct Answer: C
For a quadratic equation to have real roots, the discriminant must be non-negative. Thus, D must be greater than or equal to 0.
Q9
Hard
For which values of a, b, and c does the quadratic equation 2x² + ax + c = 0 have exactly one real root?
A. a^2 - 4(2)(c) = 0
B. a^2 - 4(2)(c) > 0
C. a^2 - 4(2)(c) < 0
D. a^2 - 4(2)(c) ≥ 0
Show Answer & Explanation
Correct Answer: A
A quadratic equation has exactly one real root when the discriminant equals zero. Therefore, we set D = 0.
Q10
Hard
For the quadratic equation ax² + bx + c = 0, if the discriminant is zero, which of the following statements is true?
A. The equation has two distinct real roots.
B. The equation has exactly one real root.
C. The equation has two complex roots.
D. The equation has no real roots.
Show Answer & Explanation
Correct Answer: B
A zero discriminant indicates that there is exactly one root (a repeated root).

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Quadratic Equations — JEE Mathematics Practice Questions Online

This page contains 1935 practice MCQs for the chapter Quadratic Equations in JEE Mathematics. The questions are organized by difficulty — 390 easy, 832 medium, 713 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 5 topics, giving you comprehensive coverage of the entire chapter.