Question

Assertion (A): If the sum of the zeros of the quadratic polynomial $$p(x)=kx^{2}+2x+3k$$, is equal to the product of its zeros then $$k=\frac{-2}{3}$$.

Reason (R): If $$\alpha$$ and $$\beta$$ be the zeros of a quadratic polynomial $$p(x)=ax^{2}+bx+c$$ then $$(\alpha+\beta)=\frac{-b}{a}$$ and $$\alpha\beta=\frac{c}{a}$$.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Both statements are true and the Reason directly provides the formulas needed. For $$p(x)=kx^{2}+2x+3k$$, the sum and product of the zeros are:

$$\alpha+\beta=-\frac{2}{k},\quad \alpha\beta=\frac{3k}{k}=3$$

Equating them:

$$-\frac{2}{k}=3\Rightarrow k=-\frac{2}{3}$$

Thus, the Reason correctly explains the Assertion.