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If a ,b are complex numbers and one of t...

If `a ,b` are complex numbers and one of the roots of the equation `x^2+a x+b=0` is purely real, whereas the other is purely imaginary, prove that `a^2- (bar a)^2=4b`.

A

`2`

B

`4`

C

`6`

D

`8`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Let us consider `alpha` as the real and `ibeta` as the imaginergy root. Then
`alpha+ibeta=-a`
`implies alpha-ibeta=-bara`
`implies2alpha=-(a+bara)` and `2ibeta=-(a-bara)`
`implies 4ialphabeta=a^(2)-bara^(2)`
`implies a^(2)-bara^(2)=4b`
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