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

Given, x x 2 + 3 | x | + 5 | x - 1 | + 6 | x - 2 | = 0 ⇒ x = 0 or x 2 + 3 | x | + 5 | x - 1 | + 6 | x - 2 | = 0 We know that sum of all positive terms can never be zero, So, x 2 + 3 | x | + 5 | x - 1 | + 6 | x - 2 | can never be zero for any value of x , So there is no value of x which satisfies the above equation Hence, only solution is x = 0 , i.e. number of solution is 1 .