The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are 2, 4 and -7
The function is given as:
f(x) = 5x³ + 5x² - 170x + 280
Factor out 5 in the function
f(x) = 5(x³ + x² - 34x + 56)
One of the roots is x + 7.
So, we have:
f(x)/(x + 7) = 5(x³ + x² - 34x + 56)/(x + 7)
Factor the expression on the right-hand side
f(x)/(x + 7) = 5((x - 2)(x - 4)(x + 7))/(x + 7)
Cancel out the common factors
f(x) = 5((x - 2)(x - 4)(x + 7)
Set the function to 0
5((x - 2)(x - 4)(x + 7) = 0
Divide through by 5
(x - 2)(x - 4)(x + 7) = 0
Expand
x - 2 = 0 or x - 4 = 0 or x + 7 = 0
Solve for x
x = 2, or x = 4 or x = -7
Hence, the roots of the function f(x) are 2, 4 and -7
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