Question

A non-zero polynomial $f\left(x\right)$ of degree $3$ has roots at $x=1,x=2$ and $x=3$. Which one of the followinng must be TRUE?

• A. $f\left(0\right)f\left(4\right)<0$
• B. $f\left(0\right)f\left(4\right)>0$
• C. $f\left(0\right)+\left(f\right(4)>0$
• D. $f\left(0\right)+\left(f\right(4)<0$

Answer 1

The correct option is A $f\left(0\right)f\left(4\right)<0$

Let us take poly as $f(x=k(x-1\left)\right(x-2\left)\right(x-3)$ where $k$ constant.
Now $f\left(0\right)=-6k(-ve)$ and $f\left(4\right)=+6k(+ve)$
$\because f\left(0\right)f\left(4\right)<0$