Question

Given below are two statements:

Statement I: If the roots of a quadratic equation are 2 and 3, then the equation is $x^2 - 5x - 6 = 0$

Statement II: If the roots of $4x^2 + 3kx + 9 = 0$ are real and distinct, then $k \le -4$ or $k \ge 4$

In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

B. Statement I: Equation with roots 2 and 3 is $x^2 - (2+3)x + (2 	imes 3) = 0 \Rightarrow x^2 - 5x + 6 = 0$. Statement I gives $x^2 - 5x - 6 = 0$, which is incorrect. Statement II: For real and distinct roots, Discriminant $D > 0$: $$(3k)^2 - 4(4)(9) > 0 \Rightarrow 9k^2 - 144 > 0 \Rightarrow k^2 > 16 \Rightarrow k < -4 	ext{ or } k > 4$$ Statement II includes equality ($k \le -4$ or $k \ge 4$), which makes roots equal when $k = \pm 4$. Thus Statement II is incorrect.

Quadratic Equations Statements

Explanation

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