Question

Solve, each of the following equation using the formula:

(ii) $x^2-10x+21=0$

Answer 1

Solve the equation

$x^2-10x+21=0$

Compare $x^2-10x+21=0$ with the equation
$a{x}^2+bx+c=0$

$a=1,b=-10\text{and}c=21$

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

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

$\Rightarrow x=\frac{-(-10)\pm \sqrt{(-10{)}^2-4\times (1)\times (21)}}{2\left(1\right)}$

$=\frac{10\pm \sqrt{100-84}}{2}$

$=\frac{10\pm \sqrt{16}}{2}$

$=\frac{10\pm 4}{2}$

$\Rightarrow x=\frac{10+4}{2}=\frac{14}{2}\text{and}x=\frac{10-4}{2}=\frac{6}{2}$

$\therefore x=7\text{and}3$.