Answer:
Zeroes: ± 6
Step-by-step explanation:
The given polynomial is: [tex]$ f(x) = 5(x + 6)^2(x - 6)^3 $[/tex].
To find the zeroes of the polynomial we equate it to zero.
⇒ [tex]$ 5(x + 6)^2(x - 6)^3 = 0 $[/tex]
⇒[tex]$ (x + 6) = 0 \hspace{5mm} or \hspace{5mm} (x - 6) = 0 $[/tex]
⇒ x = -6 and x = +6. They are the zeroes of the polynomial.
Since [tex]$ (x + 6)^2 $[/tex] is a quadratic equation it will have two roots. Therefore, the roots are x = -6, -6.
Multiplicity of a root is the number of times the root appears as the solution for the equation.
This makes x = -6 as root with multiplicity two.
Similarly, [tex]$ (x - 6)^3 $[/tex] will have three roots.
∴ x = +6, +6 , +6
x = +6 is a root with multiplicity three.
