Determine all the zeros and their multiplicities of the polynomial function. f(x) = x + 10x4...

Question

Question

math algebra

Answer 1

Answer #1

f(x) = x^5 + 10x^4 + 25x^3

To find the zeros let us equate f(x) = 0

=> x^5 + 10x^4 + 25x^3 = 0

=> x^3(x^2 + 10x + 25) = 0

=> x^3(x^2 + 2x(5) + 5^2) = 0

=> x^3(x + 5)^2 = 0

=> x = 0, x = -5

Since the degree of the term x in x^3(x + 5)^2 is 3, this implies the multiplicity of the zero at x = 0 is 3.

Since the degree of the term (x + 5) in x^3(x + 5)^2 is 2, this implies the multiplicity of the zero at x = -5 is 2.

Therefore, the correct option is

0 (multiplicity 3), -5 (multiplicity 2)

Answer 2

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