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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 option is D ac0
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

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