The number of real solutions of the equation $x(x^2+3|x|+5|x-1|+6|x-2|)=0$ is
Step-by-Step Solution
Key Concept: The equation is $x=0$ or $x^2+3|x|+5|x-1|+6|x-2|=0$. For $x\neq0$: all terms in the bracket are non-negative and at least one is positive (since $|x|,|x-1|,|x-2|$ can't all be zero simultaneously), so the bracket $>0$ for all $x\neq0$.
$x=0$ is the only solution. Answer: 1.
Correct Answer: 1