Q. Let $f(x) = x^{2} + ax + b;a,\ b \in R.If\ f(1) + f(2) + f(3) = 0,$ then the roots of the equation $f(x) = 0$
A) Are imaginary
B) Are real and equal
C) Are from the set $\left\{ 1,\ 2,\ 3 \right\}$
D) Real and distinct
Explanation
(d)
Since, $f(1) + f(2) + f(3) = 0$
$f(1)$, $f(2)$, $f(3)$ all cannot be of same sign.
$\Rightarrow$ Roots are real and distinct.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.