Question

Assertion (A): If $$(2x - 1)$$ is a factor of polynomial $$f(x)$$, then $$f\left(\frac{1}{2}\right) = 0$$. 

Reason (R): $$(ax + b)$$ is a factor of $$f(x)$$ implies $$f\left(-\frac{b}{a}\right) = 0$$.

Options

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, and R is the correct explanation of A.

Explanation:

For the factor $$2x - 1$$, here $$a = 2$$ and $$b = -1$$, so $$-\frac{b}{a} = \frac{1}{2}$$. Thus R correctly explains why $$f\left(\frac{1}{2}\right) = 0$$ when $$2x - 1$$ is a factor.