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Question

Let P(x) is polynomial of degree 4 such that P(1)=2,P(2)=5,P(3)=10 and P(4)=17 then P(5)=......

A
26
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B
50
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C
35
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D
60
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Solution

The correct option is B 50
If P(x) is polynomial of degree 4 such that,
P(1)=2,P(2)=5,P(3)=10 and P(4)=17 then,

The required polynomial is P(x)=(x1)(x2)(x3)(x4)+x2+1

Now P(5)=(51)(52)(53)(54)+52+1

P(5)=4×3×2×1+25+1

P(5)=24+26

P(5)=50

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