`2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0.`
The sum of all real roots of the equation `|x-3|^(2) +|x-3|-2 = 0 ` is

Options

A. 2
B. 3
C. 4
D. 6

Answer

D

Explanation

`|x-3|^(2) + |x-3| -2=0`
Let `|x-3|=t`
`:. t^(2) + t - 2 = 0 rArr t^(2) + 2t - t - 2 = 0 `
`rArr t(t+2) -1 (t+2) = 0 `
` rArr (t+2) (t-1) = 0 `
` rArr t=-2 or t=1` ltbr. Sinceis modulus of a number , it canot be negative .
` :. t= 1 rArr|x-3|= 1 rArr x-3 = 1 or x-3 =-1`
` rArr x=4 or 2 `
` " Sum of roots" =4+2 = 6 `.