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Let f (x) =x ^(2) + ax +b and g (x) =x ^...

Let `f (x) =x ^(2) + ax +b and g (x) =x ^(2) +cx+d ` be two quadratic polynomials with real coefficients and satisfy `ac =2 (b+d).` Then which of the following is (are) correct ?

A

Exactly one of either `f (x)=0 or g (x) =o` must have real roots.

B

Atleast one of either `f (x) =0 or g (x) =0` must have real roots.

C

Both `f (x) =0 and g (x) =0` must have real roots.

D

Both `f (x) =0 and g (x) =0` must have imaginary roots.

Text Solution

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The correct Answer is:
B
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