CMAT Exam 2023 Shift 1 Solved Paper

Question : 19 of 100

Marks: +1, -0

Given below are two statements:
Statement I : If the roots of a quadratic equation are 2 and 3 , then the equation is

x^2-5 x-6=0

Statement II: If the roots of

4 x^2+3 k x+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:

Both Statement I and Statement II are correct
Both Statement I and Statement II are incorrect
Statement I is correct but Statement II is incorrect
Statement I is incorrect but Statement II is correct

Validate

Solution:

Statement 1:

{\k}(x-2)(x-3)= {\k} (x^2-5 x+6)

is the quadratic equation whose roots are 2 and 3.
Therefore, statement 1 is incorrect.
Statement 2:
Given equation:

4 x^2+3 k x+9=0

Roots of the equation are real and distinct when the discriminant of equation is greater than zero.

\;(3 k)^2-(4)(4)(9)>0

\;(k-4)(k+4)>0

\; {\k}< -4

and

{\k}>4

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.

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