Find a second-degree polynomial p such that p (1) = 5, p' (1) = 7, and p'' (1) = 10.

Question

Nicole Rubio

Mathematics

24 April, 08:24

Find a second-degree polynomial p such that p (1) = 5, p' (1) = 7, and p'' (1) = 10.

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Answers (1)

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Rowan · Answer 1

When p (x) = ax^2 + bx + c

p' (x) = 2ax + b

p'' (x) = 2a

You require

... 2a = 10

... 2a + b = 7

... a + b + c = 5

Thus a=5, b=-3, c=3, and

... p (x) = 5x^2 - 3x + 3