Question

The graph of a quadratic polynomial $f\left(x\right)$ is shown below:


Which of the following options is/are correct?

• A. $f(-1)<0$
• B. $f\left(2\right)>0$
• C. $f(-2)>0$
• D. $f\left(1\right)=0$

Answer 1

Answer: (B), (C), (D)

$f\left(1\right)=0$

Given: $f\left(x\right)$ is a quadratic polynomial.

The graph is cutting the $x-$ axis at $x=1$
$\Rightarrow x=1$ is the only root of the equation $f\left(x\right)=0$
$\Rightarrow f\left(1\right)=0$

Also, from graph we can clearly see that $f\left(x\right)>0\forall x\in R-\left\{1\right\}$
$\therefore f\left(2\right)>0;f(-2)>0\&f(-1)>0$