Question

In the given figure $△OBC$ is an isosceles right angled triangle in which $AC$ is median, then which of the following is/are correct?

• A. The minimum value of the quadratic expression corresponding to quadratic equation is $-\frac{1}{4}$
• B. The number of solution of $f\left(|x|\right)=0$ is $4$.
• C. $|b+c|=1$
• D. The length of latus rectum of $f\left(x\right)$ is $1$.

Answer 1

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

The correct options are
A The minimum value of the quadratic expression corresponding to quadratic equation is $-\frac{1}{4}$
B The number of solution of $f\left(|x|\right)=0$ is $4$.
C $|b+c|=1$
D The length of latus rectum of $f\left(x\right)$ is $1$.

$2OA=OB=OC$
Here, $C:(0,c)\Rightarrow A:(\frac{c}{2},0)\&B:(c,0)$
$x^2+bx+c=0\frac{3c}{2}=-b,\left(\frac{c}{2}\right)\left(c\right)=c\Rightarrow c=2,b=-3f\left(x\right)=x^2-3x+2$