If the roots of `x^2-b x+c=0` are two consecutive integers, then `b^2-4c` is (a)`0` (b) `1` (c) `2` (d) none of these

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

Let the roots are `alpha` and `alpha+1`, where `alpha epsilonI`
Then sum of the roots `=2alpha+1=b`
Producrt of the roots `=alpha(alpha+1)=c`
Now `b^(2)-4c=(2alpha+1)^(2)-4alpha(alpha+1)`
`=4 alpha^(2)+1+4alpha-4alpha^(2)-4 alpha=1`
`:.b^(2)-4c=1`