Question

Find the zeros of the polynomial function and state the multiplicity of each. f(x) = 5(x + 6)2(x - 6)3

Answer 1

Answer:

Zeroes: ± 6

Step-by-step explanation:

The given polynomial is: $f(x) = 5(x + 6)^2(x - 6)^3$.

To find the zeroes of the polynomial we equate it to zero.

⇒ $5(x + 6)^2(x - 6)^3 = 0$

⇒$(x + 6) = 0 \hspace{5mm} or \hspace{5mm} (x - 6) = 0$

⇒ x = -6 and x = +6. They are the zeroes of the polynomial.

Since $(x + 6)^2$ is a quadratic equation it will have two roots. Therefore, the roots are x = -6, -6.

Multiplicity of a root is the number of times the root appears as the solution for the equation.

This makes x = -6 as root with multiplicity two.

Similarly, $(x - 6)^3$ will have three roots.

∴ x = +6, +6 , +6

x = +6 is a root with multiplicity three.