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Global Maxima

Consider a po...

Question

Consider a polynomial of degree $4$ with leading coefficient $2$ such that $P (1) = 1, P (2) = 16, P (3) = 81, P (4) = 256$ then $P (5)$ is :

673

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637

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727

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N o n e o f t h e s e

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Solution

The correct option is A $673$
$p (x) = 2 (x - 1) (x - 2) (x - 3) (x - 4) + x^{4}$
On putting x=1
P(1)=1 Which satisfies the cond?
Similarly, $P (2) = 16, P (3) = 81, P (4) = 256$
Put $x = 5$
$P (5) = 2 \times 4 \times 3 \times 2 \times 1 + (5)^{4}$
$= 48 + 625$
$P (5) = 673$

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