The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:
x = 5, x = -1 + i, x = -1 - i.
<h3>How to obtain the solutions to the equation?</h3>
The equation is defined by the rule presented as follows:
f(x) = 2x³ - 6x² - 16x - 20.
One solution for the equation is given as follows:
x = 5.
Because f(5) = 0.
Then (x - 5) is a linear factor of the function f(x), which can be written as follows:
2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).
This is because the product of a linear function and a quadratic function results in a cubic function.
Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:
2x³ - 6x² - 16x - 20 = = ax³ + (b - 5a)x² + (c - 5b)x - 5c.
Then these coefficients are obtained comparing the left and the right side of the equality as follows:
Hence the equation is:
2x² + 4x + 4.
Using a quadratic equation calculator, the remaining zeros are given as follows:
More can be learned about the solutions of an equation at brainly.com/question/25896797
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