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If the roots of x^2-bx +c=0 are two cons...

If the roots of `x^2-bx +c=0` are two consecutive integers then `b^2-4c=`

A

1

B

2

C

-2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` alpha and (alpha + 1 ) ` be the roots of equation
`x^(2) - bx + c =0 `
` :. alpha + ( alpha + 1 ) = b`
`rArr 2 alpha + 1 = b `
` and alpha ( alpha + 1 ) = c `
` Now, b^(2) - 4c = ( 2 alpha + 1 ) ^(2) - 4 [alpha ( alpha + 1 ) ]`
` = 4 alpha ^(2) + 1 + 4 alpha - 4alpha^(2) - 4 alpha = 1 `
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