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If one root of z^2 + (a + i)z+ b +ic =0 ...

If one root of `z^2 + (a + i)z+ b +ic =0` is real, where `a, b, c in R` , then `c^2 + b-ac=`

A

0

B

`-1`

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `alpha` be a real root of the given equation. Then,
`alpha^(2)+(a+i)alpha+b+ic=0`
`rArr alpha^(2)+aalpha+b=0` and `alpha+c=0` (On equating real and imag. Parts)
`rArr c^(2)-ac+b=0`
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