What is the number of real solutions of the equation x^2 - 7|x| - 18 = 0?
a) 2
b) 4
c) 3
d) 1

Hi
|x|= x for x>=0
so we get x^2-7x-18 =0
so we get (x-9)(x+2) =0
but x cannot be less than 0 so x is 9
now |x| =-x for x<0
we get x^2+7x-18=0
we get (x+9)(x-2) =0
we get x as -9 as x=2 >0 which is not possible
so we get 2 solutions

@shreyas -9 and 9 will be the only two solutions no, +2 and -2 will be rejected as x&lt;0 and x&gt;0 respectively.

In my opinion, it is 4: first take x2 - 7x - 18 and solve , you get x=-2 and 9, then take x2+7x-18 and solve, you get x=+2 and -9. Hence 4. (Mod x means you can take one time +ve and one time -ve as per basic definition of mod)