Question

Which of the following describes the zeroes of the graph of f(x) = –x^5 + 9x^4 – 18x^3?

Answer 1

Answer:

second option

Step-by-step explanation:

Given

f(x) = - $x^{5}$ + 9$x^{4}$ - 18x³

To find the zeros let f(x) = 0, that is

- $x^{5}$ + 9$x^{4}$ - 18x³ = 0 ( multiply through by - 1 )

$x^{5}$ - 9$x^{4}$ + 18x³ = 0 ← factor out x³ from each term

x³ (x² - 9x + 18) = 0 ← in standard form

x³(x - 3)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x³ = 0 ⇒ x = 0 with multiplicity 3

x - 3 = 0 ⇒ x = 3 with multiplicity 1

x - 6 = 0 ⇒ x = 6 with multiplicity 1