First slide

Theory of equations

Question

Sum of solutions of the equation $| x |^{3} - 4 | x |^{2} + 3 | x | = 0$ is

Moderate

A

4
B

3
C

0
D

1

Solution

We have $| x |^{3} - 4 | x |^{2} + 3 | x | = 0$
$\begin{array}{ll} \Rightarrow | x | (| x |^{2} - 4 | x | + 3) = 0 \\ \Rightarrow | x | (| x | - 1) (| x | - 3) = 0 \\ \Rightarrow | x | = 0, 1, 3 \\ \Rightarrow x = 0, 1, 3, - 1, - 3 \end{array}$

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