If the roots of the equationx2+bx+c=0, are two consecutive integers, then b2-4c are equal to.
-1
0
1
2
3
Explanation of correct option.
Quadratic equation:
Let α,α+1be the two consecutive integers.
∴(x+α)(x+α+1)=x2-bx+c⇒x2+xα+x+αx+α2+α=x2-bx+c⇒x2+2xα+x+α2+α=x2-bx+c⇒x2+x(2α+1)+α2+α=x2-bx+c
On comparing,
-b=2α+1c=α2+α
Now,
b2-4c=(2a+1)2-4α2+α=1
Hence, the correct answer is an option (C)
If the roots of x2−bx+c=0are two consecutive integers, then b2−4cis