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  4. A monic cubic polynomial P ( x ) satisfying the condition P (1)=1, P (3)=17 and P (5)=49 then the value of P (2), is

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Q. A monic cubic polynomial $P ( x )$ satisfying the condition $P (1)=1, P (3)=17$ and $P (5)=49$ then the value of $P (2)$, is

Complex Numbers and Quadratic Equations

Solution:

$P ( x )=( x -1)( x -3)( x -5)+2 x ^2-1 $
$P (2)=(2-1)(2-3)(2-5)+8-1=3+7=10$