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Question

Which of the following cannot be true for the given quadratic equation ax2+bx+c=0;c0 if ratio of roots of this equation is equal to it's reciprocal?

A
b0 and c is positive when a>0.
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B
b=0 and c is negative when a>0.
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C
b0 and c is negative when a<0.
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D
b=0 and c is negative when a<0.
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Solution

The correct option is D b=0 and c is negative when a<0.
Let p,q be the roots of the given equation.
According to the given condition,
pq=qpp2=q2p=±q

Case 1:
a>0 and p=q, b0 and c is positive.

Case 2:
a>0 and p=q, b=0 and c is negative.

Case 3:
a<0 and p=q, b0 and c is negative.

Case 4:
a<0 and p=q, b=0 and c is positive.

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