Question

If $f\left(x\right)$ and $g\left(x\right)$ are two polynomials with integral coefficients which vanish at $x=\frac{1}{2}$, then what is the factor of HCF of $f\left(x\right)$ and $g\left(x\right)$?

• A. $x-1$
• B. $x-2$
• C. $2x-1$
• D. $2x+1$

Answer 1

The correct option is C $2x-1$

Given, $x=\frac{1}{2}$

$\Rightarrow (2x-1)=0$
Therefore, $(2x-1)$ is satisfying both $f\left(x\right)$ and $g\left(x\right)$, so $(2x-1)$ is the factor of H.C.F. of $f\left(x\right)$ and $g\left(x\right)$.