Question

Solve each of the following equations for x and give, in each case, your answer correct to one decimal place:

(ii) $5x^2+10x-3=0$

Answer 1

Compare $5x^2+10x-3=0$ with the equation $a{x}^2+bx+c=0$

$a=5,b=10andc=-3$

We know that, for the equation $a{x}^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ are the roots of the equation

$x=\frac{-\left(10\right)\pm \sqrt{(10{)}^2-4(5\left)\right(-3)}}{2\left(5\right)}$

$=\frac{-10\pm \sqrt{100+60}}{10}$

$=\frac{-10\pm 12.6}{10}$

$x=\frac{-10+12.6}{10}andx=\frac{-10-12.6}{10}$

$x=\frac{2.6}{10}andx=\frac{-22.6}{10}$

$x=0.26andx=-2.26$

$\therefore$ The roots of the given equation correct to one decimal place are $0.3$ and $-2.3$.