Question

If both roots of the equation $g\left(x\right)=0$ are greater than $-1,$ then sum of roots lies in the interval :

• A. $(-\infty ,-2)$
• B. $(-\infty ,\frac{-1}{4})$
• C. $(-2,\infty )$
• D. $(\frac{-1}{2},\infty )$

Answer 1

The correct option is C $(-2,\infty )$

Say $g\left(x\right)$ has two roots, $a,b$

Given,

$a>-1$..............(1)

$b>-1$..............(2)

Equation (1) + (2) gives

$(a+b)>-2$

$⟹$ Sum of roots lies in $(-2,\infty )$