Question

If $x-2$ and $x-\frac{1}{2}$ both are the factors of the polynomial $n{x}^2-5x+m$, then $m=n=2$

• A. True
• B. False

Answer 1

The correct option is A True

Let $f\left(x\right)=n{x}^2-5x+m$

$x-2$ and $x-1/2$ are factors of $f\left(x\right)$ then $x=2$ and $x=\frac{1}{2}$ are roots of

equation $f\left(x\right)$

Now, we know $\Rightarrow$

Product of roots = $\frac{m}{n}=\left(2\right)\times \left(\frac{1}{2}\right)$

$\Rightarrow \frac{m}{n}=1$

$\Rightarrow m=n$

and

sum of roots = $-(-5)=2+\frac{1}{2}=\frac{5}{2}$

$\Rightarrow \frac{5}{n}=\frac{5}{2}\Rightarrow n=2$

$\therefore m=n=2$ Hence proved