perplexus.info :: Calculus : Find Function, Given that the Sum is Quartic

Find Function, Given that the Sum is Quartic (Posted on 2024-05-01)

P(x) is a polynomial such that:
P(x) + P'(x) + P"(x) = x⁴

Find P(x)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

Comment 1 of 1

P(x) = x^4 + ax^3 + bx^2 + cx + d

P'(x) = 4x^3 + 3ax^2 + 2bx + c

P''(x) = 12x^2 + 6ax + 2b

a + 4 = 0 a = -4

b + 3a + 12 = 0 b = 0

c + 2b + 6a = 0 c = 24

d + c + 2b = 0 d = -24

P(x) = x^4 - 4x^3 + 24x - 24

Posted by Larry on 2024-05-01 13:00:24

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