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The roots of the equation x^2+ px +q=0 a...

The roots of the equation `x^2+ px +q=0` are consecutive integers. Find the discriminant of the quadratic equation.

Text Solution

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Let roots of the given quadratic equation are `alpha,alpha+1`.
Then, `alpha+alpha+1 = -p`
`=>2alpha = -p-1 => alpha = -((p+1)/2)`
Now, `alpha(alpha+1) = q`
`=>alpha^2+alpha = q`
`=>(p+1)^2/4-((p+1)/2) = q`
`=>(p+1)/2((p+1)/2-1) = q`
`=>(p+1)/2((p-1)/2) = q`
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