Question

Is $x=-2$ a solution of the equation $x^2-2x+8=0$?

Answer 1

Step 1: State the factor theorem.

Given equation: $x^2-2x+8=0$.

Let the quadratic equation denoted by $p\left(x\right)=0$, here, $p\left(x\right)=x^2-2x+8$.

If, $a$ is a solution to the equation $p\left(x\right)=0$, then $p\left(a\right)=0$.

Step 2: Apply the factor theorem.

Put $x=-2$ in the given equation.

$$\begin{gathered} p\left(-2\right)={\left(-2\right)}^2-2·\left(-2\right)+8 \\ \Rightarrow p\left(-2\right)=4+4+8 \\ \Rightarrow p\left(-2\right)=16 \end{gathered}$$

$p\left(-2\right)\ne 0$.

Hence, $x=-2$ is not a solution to the given equation.