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Question

If P(x)=ax2+bx+c and Q(x)=ax2+dx+c, where ac0 [a, b, c, d are all real], then P(x).Q(x) = 0 has

A
at least two real roots
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B
two real roots
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C
four real roots
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D
no real root
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Solution

The correct option is A at least two real roots
P(x)=ax2+bx+cQ(x)=ax2+dx+cD1=b24acD2=d2+4ac

If ac is negative, then D1 will have 2 real roots (D2 too can have real roots)

If ac is positive,then D2 will have 2 real roots (D1 too can have real roots)

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