Question

Solve each of the following equations for x and give, in each case, your answer correct to 2 decimal places:

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

Answer 1

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

$a=2,b=-10andc=5$

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

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

$\Rightarrow x=\frac{10\pm \sqrt{100-40}}{4}$

$\Rightarrow x=\frac{10\pm \sqrt{60}}{4}$

$\Rightarrow x=\frac{10\pm 7.75}{4}$

$\Rightarrow x=\frac{10+7.75}{4}andx=\frac{10-7.75}{4}$

$\therefore x=4.44and0.56$.