If `a ,b ,c` are three distinct positive real numbers, the number of real and distinct roots of `a x^2+2b|x|-c=0` is `0` b. `4` c. `2` d. none of these

Options

A. 4
B. 2
C. 0
D. none of these

Answer

B

Explanation

We have, `ax^(2) + 2b |x| - c = 0`
`rArr" "a|x|^(2)+2b|x|-c = 0`
`rArr" "|x|=(-2b +- sqrt(4b^(2)+4ac))/(2a)`
`rArr" "|x|=(-b +- sqrt(b^(2)+ac))/(a)`
`rArr" "|x|=(-b+sqrt(b^(2)+ac))/(a)`
`rArr" "x = +- (-b+sqrt(b^(2) + ac))/(a)`