Question

Solve the quadratic equation $x^2-17x+70=0$ by using the quadratic formula.

Answer 1

Determining the value of $x$ by using the quadratic formula

The quadratic formula is $\begin{array}{rcl}x& =& \frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$.

For the given equation $x^2-17x+70=0$, the value of variables are $a=1,b=-17$ and $c=70$.

Substituting the values of $a,b$ and $c$ in quadratic formula,

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \Rightarrow x=\frac{-(-17)\pm \sqrt{{(-17)}^2-4\left(1\right)\left(70\right)}}{2\left(1\right)} \\ \Rightarrow x=\frac{17\pm \sqrt{{17}^2-280}}{2} \\ \Rightarrow x=\frac{17\pm \sqrt{289-280}}{2} \\ \Rightarrow x=\frac{17\pm \sqrt{9}}{2} \\ \Rightarrow x=\frac{17-3}{2},\frac{17+3}{2} \\ \Rightarrow x=\frac{14}{2},\frac{20}{2} \end{gathered}$$

$\therefore x=7,10$

Therefore, the roots of the given equation are $7$, $10$.