Question

The equation $x^2-3\left|x\right|+2=0$ has

• A. No real root
• B. One real root
• C. Two real root
• D. Four real root

Answer 1

The correct option is D

Four real root

Explanation for the correct answer:

Find the number of roots of the given equation.

A equation $x^2-3\left|x\right|+2=0$ is given.

Rewrite the given equation as follows:

${\left|x\right|}^2-3\left|x\right|+2=0$

Find the roots of the above equation using quadratic formula.

$$\begin{gathered} \left|x\right|=\frac{3\pm \sqrt{3^2-4·1·2}}{2·1} \\ \Rightarrow \left|x\right|=\frac{3\pm \sqrt{9-8}}{2} \\ \Rightarrow \left|x\right|=\frac{3\pm \sqrt{1}}{2} \\ \Rightarrow \left|x\right|=\frac{3\pm 1}{2} \\ \Rightarrow \left|x\right|=\{1,2\} \end{gathered}$$

Since, values of $\left|x\right|$ are $\{1,2\}$.

Therefore, values of $x$ are $\left\{-2,-1,1,2\right\}$.

So, there are four roots of the given equation.

Hence, option $D$ is correct .