Question

If the roots of $x^2+bx+c=0$ are two consecutive integers, then $b^2-4c=$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$1$

Let the roots be $n$ and $n+1$

$\Rightarrow$ sum of roots $=\frac{-b}{1}=-b=n+n+1$

$2n+1=-b$

Product of roots $=c=n(n+1)$

$n=\frac{-(b+1)}{2}$

$c=\frac{-(b+1)}{2}(-\left(\frac{b+1}{2}\right)+1)$

$=-\left(\frac{1-b}{2}\right)\left(\frac{1+b}{2}\right)$

$=-\left(\frac{1-b^2}{4}\right)$

$\Rightarrow b^2-4c=1$