Question

Algebraically, find all remaining zeros of f(x) = 8x^3 - 6x^2-36x +27 in simplest form.

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Answer 1

`x=-(3√(2))/(2),(3)/(4),(3√(2) )/(2)`

Explanation:

Given expression is,

f(x) = 8x³ - 6x² - 36x + 27

For zeros of the function,

f(x) = 0

8x³ - 6x² - 36x + 27 = 0

2x²(4x - 3) - 9(4x - 3) = 0

(2x² - 9)(4x - 3) = 0

(2x² - 9) = 0

x² =
`(9)/(2)`

x =
`\pm(3)/(√(2))`

x =
`\pm (3√(2))/(2)`

Or (4x - 3) = 0

x =
`(3)/(4)`

Therefore, all zeros of the given functions are
`x=-(3√(2))/(2),(3)/(4),(3√(2) )/(2)`.