Question

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$\frac{m}{n}{x}^2+\frac{n}{m}=1-2x$

Answer 1

The given equation $\frac{m}{n}{x}^2$ + $\frac{n}{m}$ = $1-2x$
$\to$ $\frac{m^2{x}^2+n^2}{mn}=1-2x$

$\to$ $m^2{x}^2+n^2=mn(1-2x)$

$\to$ $m^2{x}^2+n^2=mn-2mnx$

$\to$ $m^2{x}^2+n^2-2mnx=mn$
$\to$ $m^2{x}^2+2mnx+n^2=mn$

$\to$ $(mx+n{)}^2=mn$

$\to$ $mx+n=\pm \sqrt{mn}$

$\to$ $mx=-n+\pm \sqrt{mn}$

Either $x$ = $\frac{-n+\sqrt{mn}}{m}$ or $x$ = $\frac{-n-\sqrt{mn}}{m}$