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Question

If P(x)=ax2+bx+c and Q(x)=ax2+dx+c , ac0, then the equation P(x).Q(x)=0 has

A
two imaginary roots
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B
more than two imaginary roots
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C
atleast two real roots
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D
no real roots
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Solution

The correct option is C atleast two real roots
P(x)=ax2+bx+c
Hence, for real roots,
b24ac0
Q(x)=ax2+dx+c
Hence, for real roots,
d2+4ac0
Now,
ac0
Now if ac<0
Then,
b24ac>0
Hence, P(x).Q(x) has atleast 2 real roots .
If ac>0
Then
d2+4ac>0
Hence, P(x).Q(x) has atleast 2 real roots .

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