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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=`

Text Solution

Verified by Experts

The correct Answer is:
`b^(2) - 4c = 1`
Let `alpha , alpha + 1` be the roots of `x^(2) - bx + c = 0` where `alpha in `Z .
` therefore alpha + (alpha +1) = b` (1)
` alpha (alpha +1) = c` (2)
Form (1), we have
` alpha = (b-1)/(2)`
Putting in Eq.(2), we have
`((b-1)/(2)) ((b-1)/(2) +1) = c`
or (b^(2) -1)/(4) = c`
or `b^(2) -1 = 4c`
or b^(2) - 4c = 1`
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