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  4. If y=a x2+b x+c represents a parabola with vertex A as shown in the figure and b2=2(b+2 a c), where a ≠ 0 and AP =3, then OP equals ( O is origin)

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Q. If $y=a x^2+b x+c$ represents a parabola with vertex $A$ as shown in the figure and $b^2=2(b+2 a c)$, where $a \neq 0$ and $AP =3$, then $OP$ equals ( $O$ is origin)Mathematics Question Image

Complex Numbers and Quadratic Equations

Solution:

$b ^2=2 b +4 ac \Rightarrow 4 ac - b ^2=-2 b $
$\Rightarrow AP = OP =3$