Question 19

# Given below are two statements: Statement I : If the roots of a quadratic equation are 2 and 3, then the equation is $$x^{2} - 5x- 6 = 0$$Â Statement II: If the roots of $$4x^{2}+3kx + 9 = 0$$ are real and distinct, then $$k \leq - 4$$ or $$k \geq 4$$In the light of the above statements, choose the most appropriate answer from the options given below:

Solution

Statement 1:

k$$(x-2)(x-3)$$ = k($$x^2-5x+6$$) is the quadratic equation whose roots are 2 and 3.

Therefore, statement 1 is incorrect.

Statement 2:

Given equation:Â $$4x^{2}+3kx + 9 = 0$$

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

$$\left(3k\right)^2-\left(4\right)\left(4\right)\left(9\right)>0$$

$$\left(k-4\right)\left(k+4\right)>0$$

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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