The number of real solutions of the equation x(x^2 + 3|x| + 5|x−1| + 6|x−2|) = 0 is ______.

Question

The number of real solutions of the equation \(\mathrm{x}\left(\mathrm{x}^{2}+3|\mathrm{x}|+5|\mathrm{x}-1|+6|\mathrm{x}-2|\right)=0\) is _____.

Answer 1

Correct answer: 1

\(\mathrm x=0\) and \(\mathrm{x}^{2}+3|\mathrm{x}|+5|\mathrm{x}-1|+6|\mathrm{x}-2|=0\)

Here all terms are +ve except at \(\mathrm x = 0\)

So there is no value of \(\mathrm x\)

Satisfies this equation

Only solution \(\mathrm x = 0\)

No of solution 1.