Which of the following equations has maximum number of real roots ?

Options

A. `x^2-|x| - 2= 0`
B. `x^2-2|x|+3=0`
C. `x^2-3|x|+2=0 `
D. `x^2+3|x|+2=0`

Answer

c

Explanation

`x^2-|x| -2 = 0 `
`rArr |x|^2-|x| -2 =0 `
`rArr (|x| -2 )(|x| +1 )=0 `
`rArr |x | = 2 rArr x = pm 2`
`x^2-2|x|+3=0 `
Thus, `|x|^2-2|x|+3=0` has no roots as discriminant is negative `x^2-3|x|+2=0`
`rArr x^2|x|-3 |x| + 2 +0`
`rArr |x|^2-3|x|+2`
`rArr (|x|-2)(|x|-1)=0`
`rArr |x|=1,2 rArr x = pm 1,pm2.`
`x^2+3|x|+2=0`
`rArr |x|^2+3|x|+2=0`
`rArr (|x|+2)(|x|+1)=0`
`rArr |x|=-1,-2 ("not possible" )`
Thus , the equation ( c) has maximum real roots ,