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Question

If the roots of the equation x2ax+b=0 are real and differ by a quantity which is less than c(c>0), then b lies between

A
a2c24 and a24
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B
a2+c24 and a24
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C
a2c22 and a24
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D
None of these
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Solution

The correct option is B a2c24 and a24
Let roots be α,β
|αβ|<c(α+β)24αβ<c
So, a24b<c2
b>a2c24
and since b<a24 {max value of x2ax+b=0}
So, b lies between a2c24 and a24

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