Question

3^1/2 and -3^1/2 are the zeroes of f(x)= x^4 -3x^3 -x^2 +9x -6. Find all the zeroes of f(x).

Answer 1

Answer:

Zeroes of f(x) are: 1, 2, ± √3

Step-by-step explanation:

y = x^4 - 3x³ - x² + 9x - 6  = (x -1)(x³ - 2x² - 3x + 6) = (x -1)(x - 2)(x² - 3) =

(x -1)(x - 2)(x - √3)(x + √3)

(x^4 - 3x³ - x² + 9x - 6) ÷ (x - 1) = x³ - 2x² - 3x + 6

(x³- 2x - 3x +6) ÷ (x - 2) = x² - 3

x² - 3 = (x - √3)(x + √3)

f(x) = (x -1)(x - 2)(x - √3)(x + √3)

Zeroes of f(x) are: 1, 2, ± √3