Question

Assertion (A): A monic quadratic polynomial having 4 and –2 as its zeros is $$\left(x^{2}-2x-8\right)$$.

Reason (R): The monic quadratic polynomial having $$\alpha$$ and $$\beta$$ as its zeros, is given by $$x^{2}-(\alpha+\beta)x+\alpha\beta$$.

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 Assertion (A) and Reason (R) are true.

Using the stated formula with zeros 4 and –2:

$$\alpha+\beta=4+(-2)=2,\quad \alpha\beta=4(-2)=-8$$

$$p(x)=x^{2}-2x-8$$

Thus, the Reason correctly explains the Assertion.