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Question

If the roots of x2bx+c=0are two consecutive integers, then b24cis


A

0

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B

1

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C

2

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D

none of these

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Solution

The correct option is B

1


Given equation: x2bx+c=0

Let α and α+1 be the two consecutive roots of the equation.

Sum of the roots = α+α+1=2α+1

Product of the roots = α(α+1)=α2+α

So, sum of the roots = 2α+1 =Coefficient of xCoefficient of x2=b1=b

Product of the roots =α2+α=Constant termCoeffecient of x2=c1=c

Now, b24c=(2α+1)24(α2+α)=4α2+4α+14α24α=1


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