F is a polynomial of degree 6. f has a root of multiplicity

Mathematics

1 answer:

frutty [35]3 years ago

4 0

Answer:

f(x) = 0.43 * $(x - 3)^{2}$ * $(x-1)^{3}$ *(x + 10)

Step-by-step explanation:

We have a 6th degree polynomial f(x)

r = 3 is a root of f with multiplicity 2

r = 1 is a root of f with multiplicity 3

f(-5) = -29721.6

f(-10) = 0

Then: f(x) = a*((x -3)^2 ) * ((x - 1)^3)*(x + 10)

f(-5) = a * (-8)^2 * (-6)^3 * (5) = -29,721.6

a* (64) * (-216)* 5 = -29,721.6

-a*69,120 = -29,721.6

a = -29,721.6/-69,120

a = 0.43

f(x) = 0.43 * $(x - 3)^{2}$ * $(x-1)^{3}$ *(x + 10)

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