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Question

If a>0 and the equation ax2+bx+c=0 has two real roots α and β such that |α|1, |β|1, then
 



A

a+b+c0
 

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B

ab+c0
 

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C

a+|b|+c0
 

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D

ac0

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Solution

The correct options are
A

a+b+c0
 


B

ab+c0
 


C

a+|b|+c0
 


D

ac0


Given y=ax2+bx+c, a>0
As both the roots lie in the interval [-1,1], we have 
y(1)0,y(1)0ab+c0,a+b+c0a+|b|+c0Also, αβ|αβ|=|α||β|1ca1 or c a or ac0


Mathematics

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