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Let P(x) be a cubic polynomial such that...

Let P(x) be a cubic polynomial such that coefficient of `x^3` is 1 `, p(1) = 1, p(2) = 2, p(3) = 3 then the value of p(4) is :

Text Solution

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Let `P(x) = x^3+ax^2+bx+c`
Then, `P(1) = 1+a+b+c = 1`
`=> a+b+c = 0->(1)`
`P(2) = 8+4a+2b+c = 2=> 4a+2b+c = -6->(2)`
`P(3) = 27+9a+3b+c = 3=>9a+3b+c = -24->(3)`
Subtracting (1) from (2)
`3a+b = -6->(4)`
Subtracting (2) from (3)
...
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