Question

If $k\in R$ lies between the roots of $a{x}^2+bx+c=0,a<0$. Consider $f\left(x\right)=a{x}^2+bx+c=0$, then $f\left(k\right)$ $\&$

• A. $D\ge 0$
• B. $>0$
• C. $<0$
• D. $D>0$

Answer 1

Answer: (A), (B)

$>0$

Let $\alpha ,\beta$ are roots of $a{x}^2+bx+c=0$
and $k\in R$ such that $\beta <k<\alpha$
We can draw the graph of $f\left(x\right)=a{x}^2+bx+c;a<0$ as:


Now, from the graph, we can observe some conditions that are:
$A.D>0$
$B.f\left(k\right)>0$