Question

The zeroes of $mn(x^2+1)=(m^2+n^2)x$ are:

• A. $\frac{m}{n}and\frac{n}{m}$
• B. $\frac{-m}{n}and\frac{n}{m}$
• C. $\frac{-m}{n}and\frac{-n}{m}$
• D. $\frac{m}{n}and\frac{-n}{m}$

Answer 1

The correct option is A $\frac{m}{n}and\frac{n}{m}$

Given polynomial, $mn(x^2+1)=(m^2+n^2)x$

Let's factorise it.
$mn{x}^2-(m^2+n^2)x+mn=0$

$\Rightarrow mn{x}^2-m^{2}x-n^{2}x+mn=0$

$\Rightarrow mx(nx-m)-n(nx-m)=0$

$\Rightarrow (mx-n)(nx-m)=0$

$\Rightarrow mx-n=0ornx-m=0$

$\Rightarrow x=\frac{m}{n}or\frac{n}{m}$

So, zeroes of the given polynomial are $\frac{m}{n}$ and $\frac{n}{m}$.