Question

# If roots of the equation $$x^2-bx+c=0$$ be two consecutive integers, then $$b^2-4c$$ equals :

A
2
B
3
C
2
D
1

Solution

## The correct option is D $$1$$Given equation is $$x^2-bx+c=0$$Let the roots be $$\alpha$$ and $$\alpha+1$$Therefore, $$2\alpha+1=b$$$$\Rightarrow \alpha(\alpha+1)=c$$Hence, $$b^2-4c$$$$=(2\alpha+1)^2-4\alpha(\alpha+1)$$$$=1$$Mathematics

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