Question

Assertion (A): The quadratic polynomial whose zeros are $$(3+\sqrt{2})$$ and $$(3-\sqrt{2})$$ is given by $$p(x)=(x^{2}-6x+7)$$.

Reason (R): If $$\alpha$$ is a zero of the quadratic polynomial $$p(x)$$ then $$(x-\alpha)$$ is a factor of $$p(x)$$.

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 but Reason (R) is not a correct explanation of Assertion (A).

Explanation:

Both statements are true.

The sum and product of the given zeros are:

$$\alpha+\beta=(3+\sqrt{2})+(3-\sqrt{2})=6$$

$$\alpha\beta=(3+\sqrt{2})(3-\sqrt{2})=9-2=7$$

Hence, the polynomial is $$x^{2}-6x+7$$. The Reason is the factor theorem, but it does not explain how this polynomial is obtained from the zeros; therefore, it is not the correct explanation.