Question

Question 1(iii)
Find the roots of the following quadratic equations by factorisation:
(iii) $\sqrt{2}{x}^2+7x+5\sqrt{2}=0$

Answer 1

(iii) $\sqrt{2}{x}^2+7x+5\sqrt{2}$
$=\sqrt{2}{x}^2+5x+2x+5\sqrt{2}$(Splitting the middle term 7x as 5x+2x because $5x\times 2x=10x^2$)
$=x(\sqrt{2}x+5)+\sqrt{2}(\sqrt{2}x+5)=(\sqrt{2}x+5)(x+\sqrt{2})$
Roots of this equation are the values for which $(\sqrt{2}x+5)(x+\sqrt{2})=0$
$\therefore \sqrt{2}x+5=0orx+\sqrt{2}=0$
$\Rightarrow x=-\frac{5}{\sqrt{2}}orx=-\sqrt{2}$