Which of the following cannot be true for the given quadratic equation ax2+bx+c=0;c≠0 if ratio of roots of this equation is equal to it's reciprocal?
A
b≠0 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
b≠0 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 Db=0 and c is negative when a<0. Let p,q be the roots of the given equation. According to the given condition, pq=qp⇒p2=q2⇒p=±q
Case 1: a>0 and p=q, b≠0 and c is positive. Case 2: a>0 and p=−q, b=0 and c is negative. Case 3: a<0 and p=q, b≠0 and c is negative. Case 4: a<0 and p=−q, b=0 and c is positive.