If $a, b, c \in \mathbb{R}$ and quadratic equation $x^2+(a+b) x+c=0$ has no real roots, then

Question

Professor PC Thomas Classes · Answer

$\Delta = (a+b)^2 - 4c < 0$. Function $f(1)=1+a+b+c$ and $f(-1)=1-a-b+c$ share same sign. Evaluating conditions gives Option B.