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

Answer:

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.

Step-by-step 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 $g(1) < 0$.