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Question

Let f(x)=ax2+bx+c,a,b,cR. If f(x) takes real values for real values of x and non-real values for non-real values of x, then

A
a=0
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B
b=0
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C
c=0
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D
Nothing can be said about a,b,c
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Solution

The correct option is A a=0
f(x) takes real values for real values of x non real values for non real values of x

If 2nd degree term exists in the question for non real multiple of icancels with rest of the equation and gives us the real term

Here the only condition is 2nd degree coefficient must be zero

a=0

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