Question

A student says that if $5x^2=20$, then $x$ must be equal to $2$. do you agree or disagree with the student? justify your answer.

Answer 1

Solve the quadratic equation:

Divide both sides of the given equation by $5$,

$\begin{array}{rcl}\frac{5x^2}{5}& =& \frac{20}{5}\\ & \Rightarrow & x^2=4\end{array}$

Take square root of both sides,

$\begin{array}{rcl}\sqrt{x^2}& =& \sqrt{4}\\ x& =& \pm 2\end{array}$

So, the solutions of the given equation are $\pm 2$.

Since the student has forgot to consider the $-2$ as solution, the student's statement is wrong.

Hence,the student's statement is wrong.