Question

Find the zeros f(x) = x 3 - 3x 2 – 5x +15

Answer 1

x = ±
`√(5)` x = 3

Explanation:

to find the zeros set f(x) = 0 , that is

x³ - 3x² - 5x + 15 = 0 ( factor the first/second and third/fourth terms )

x²(x - 3) - 5(x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(x² - 5) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x² - 5 = 0 ( add 5 to both sides )

x² = 5 ( take square root of both sides )

x = ±
`√(5)`

the zeros of f(x) are then

x = -
`√(5)` , x =
`√(5)` , x = 3