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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 


Your Answer
A
a>0,  b>0 and c<0
Your Answer
B
a<0,  b<0 and c>0
Correct Answer
C
b>0,  c>0 and a<0 
Correct Answer
D
b<0,  c<0 and a>0 

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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