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Question

The number of cubic polynomials P(x) satisfying P(1)=2,P(2)=4,P(3)=6,P(4)=8 is

A
0
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B
1
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C
more than one but finitely many
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D
infinitely many
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Solution

The correct option is A 0
Let f(x)=2x.
Now according to the question, f(x) and P(x) intersect at four points (x=1,x=2,x=3,x=4), which is not possible.
So, no such cubic polynomial exists.

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