If P ( x ) = a x 2 + b x + c and Q ( x ) = − a x 2 + d x + c where a c  = 0 , then P ( x ) ⋅ Q ( x ) = 0 has at least

Question

If P ( x ) = a x 2 + b x + c and Q ( x ) = − a x 2 + d x + c where a c  = 0 , then P ( x ) ⋅ Q ( x ) = 0 has at least, Four real roots, Two real roots, Four imaginary roots, None of these

MARKS App · Accepted Answer

Let all four roots are imaginary. Then roots of both equations P ( x ) = 0 and Q ( x ) = 0 are imaginary. Thus b 2 − 4 a c 0 ; d 2 + 4 a c 0 , So b 2 + d 2 0 which is impossible unless b = 0 , d = 0

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