Question

Factorise.
$2x^2+x-45$

Answer 1

Consider $2x^2+x-45$

Factor formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here $a=2,b=1,c=-45$

$\therefore x=\frac{-1\pm \sqrt{1+360}}{4}$

$=\frac{-1\pm \sqrt{361}}{4}$

$=\frac{-1\pm 19}{4}$

$\therefore x=\frac{-1+19}{4},\frac{-1-19}{4}$

$\Rightarrow x=\frac{18}{4},\frac{-20}{4}$

$\Rightarrow x=\frac{9}{2},-5$

$\therefore 2x^2+x-45=(2x-9)(x+5)$