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Q.
If $p$ is the root of the equation $x^2-2 x-6=0$, then the value of $\frac{p^3-2 p^2-4 p+7}{p^2+1}$ is
Complex Numbers and Quadratic Equations
Solution:
$ p^2-2 p-6=0$
$\frac{ p ^3-2 p ^2-4 p +7}{ p ^2+1}=\frac{ p \left( p ^2-2 p \right)-4 p +7}{ p ^2+1} $
$=\frac{2 p +7}{ p ^2+1}=\frac{2 p +7}{2 p +7}=1 $