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Question

If the roots of the quadratic equation ax2+bx+c=0 are opposite in sign and positive root is greater in magnitude, then

A
a>0, b>0 and c<0
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B
a<0, b<0 and c>0
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C
b>0, c>0 and a<0
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D
b<0, c<0 and a>0
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Solution

The correct options are
C b>0, c>0 and a<0
D b<0, c<0 and a>0
Given equation ax2+bx+c=0
Let the roots be α,β
Assuming the greater root to be β
So, β>0α<0
Now,
α+β>0ba>0ba<0
So, a,b are of opposite sign.
α×β<0ca<0
So, a,c are of opposite sign.

Therefore,
b,c>0 and a<0
b,c<0 and a>0

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