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If A=(x in R:x^(2)-5|x|+6=0}, then n(A)=...

If `A=(x in R:x^(2)-5|x|+6=0}`, then n(A)= . . .

A

2

B

0

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `x^(2)-5|x|+6=0`
`impliesx^(2)-3|x|-2|x|+6=0`
`implies|x|(|x|-3)-2(|x|-3)=0`
`implies(|x|-2)(|x|-3)=0`
`implies|x|-2=0` or `|x|-3=0`
`implies|x|=2` or `|x|=3`
`impliesx=-2,2` or `x=-3,3`
`thereforen(A)=4`.
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