The roots of the given polynomial function are 1, (2 + √12)2, (2 - √12)2.
What is a function?
A function relates the domain set to the range set. For any particular function, for a value in the domain set, there must be a value in the range set.
The given function:
f(x)
= x³ - 3x² + 2
= x²(x - 1) - 2x(x - 1) - 2(x - 1)
= (x² - 2x -2)(x - 1)
In order to find the roots of the equation, we need to take the value of the function as zero.
Therefore, (x² - 2x -2)(x - 1) = 0
⇒ (x - 1) = 0; or, (x² - 2x -2) = 0
When, (x - 1) = 0
⇒ x = 1
When, (x² - 2x -2) = 0
⇒ x
= [- (- 2) ± [{√(- 2)² - 4 × 1 × (- 2)}]]/2 × 1
= [ 2 ± [√(4 + 8)]/2
= [2 ± [√(12)]/2
Learn more about a function here: https://brainly.com/question/11828649
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