Quadratic Equations Actual Question in CMAT 2023 Slot – 1

Q1. Given below are two statements:
Statement I : If the roots of a quadratic equation are 2 and 3, then the equation is x² − 5x − 6 = 0

Statement II: If the roots of 4x² + 3kx + 9 = 0 are real and distinct, then k ≤ −4 k ≥ 4

In the light of the above statements, choose the most appropriate answer from the options given
below:
A. Both Statement I and Statement II are correct
B. Both Statement I and Statement II are incorrect
C. Statement I is correct but Statement II is incorrect
D. Statement I is incorrect but Statement II is correct

EXPLANATION

Answer: B
Explanation:
Statement 1: k(x − 2)(x − 3) k(x² – 5x + 6) is the quadratic equation whose roots are 2 and 3.
Therefore, statement 1 is incorrect.
Statement 2: Roots of the equation are real and distinct when the discriminant of equation is greater than zero.

But in the given statement, equal to sign is also considered which is incorrect. If discriminant is equal to zero, roots of the equation are equal. Therefore, statement 2 is incorrect. The answer is option B.