Question

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

(i) $x^2-8x+5=0$

Answer 1

Compare $x^2-8x+5=0$ with the equation $a{x}^2+bx+c=0$

$a=1,b=-8andc=5$

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

$x=\frac{-(-8)\pm \sqrt{(-8{)}^2-4(1\left)\right(5)}}{2\left(1\right)}$

$=\frac{8\pm \sqrt{64-20}}{2}$

$=\frac{8\pm \sqrt{44}}{2}$

$=\frac{8\pm 2\sqrt{11}}{2}$

$x=4+3.3andx=4-3.3$

$\therefore x=7.3and0.7$