Question

Two of the zeros of g(x) are specifically listed in the table. What are those two zeros? Then, what is the multiplicity of each zero? Give a reason for your response to both questions

Answer 1

a)
`x = -1` and
`x = 2` are roots of the polynomial
`g(x) = a\cdot x^(3)+5\cdot x^(2)+4\cdot x + c`.

b)
`x = -1` and
`x = 2` have a multiplicity of 1.

Explanation:

a) What are those two zeroes?

The two values of
`x` listed in the table whose outputs are zero are roots of
`g(x)`, defined as
`g(x) = a\cdot x^(3)+5\cdot x^(2)+4\cdot x + c`. In other words, those values of
`x` (-1 and 2) satisfies the condition that
`g(x) = 0`.

b) What is the multiplicity of each zero?

From the Fundamental Theorem of Algebra, we know that third-order polynomials have three roots and from we understand that those two known zeroes with a multiplicity of 1, since there is a third root within
`0 < x < 1`, where
`g(0) > 0` and
`g(1) < 0`.