Question

The roots of $x^2+bx+c=0$ are both real and greater than $1$. Let $x=b+c+1$. Then $s$

• A. May be less than zero
• B. May be equal to zero
• C. Must be greater than zero
• D. Must be less than zero
• E. Must be between $-1$ and $+1$

Answer 1

Answer: (C)

Must be greater than zero

Let the roots be $1+m$ and $1+n$, $m\&n$ both positive.

$1+m+1+n=-b$

$(1+m)(1+n)=c$

$S=b+c+1$

$=-(1+m+1+n)+(1+m+n+mn)+1$

$=mn$

$mn>0$

So,$S>0$

Must be greater than zero.