Question

Solve the quadratic equation $x^2-8x+15=0$ 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 $x^2-8x+15=0$, the value of variables are $a=1,b=-8$ and $c=15$.

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

$$\begin{gathered} \Rightarrow x=\frac{-(-8)\pm \sqrt{{(-8)}^2-4\left(1\right)\left(15\right)}}{2\left(1\right)} \\ \Rightarrow x=\frac{8\pm \sqrt{64-60}}{2} \\ \Rightarrow x=\frac{8\pm \sqrt{4}}{2} \\ \Rightarrow x=\frac{8\pm 2}{2} \\ \Rightarrow x=\frac{8-2}{2},\frac{8+2}{2} \\ \therefore x=3,5 \end{gathered}$$

Therefore, the roots of the given equation are $3$, $5$.