If the roots of x2−bx+c=0are two consecutive integers, then b2−4cis
Given equation: x2−bx+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