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One factor of f (x ) = 5 x cubed 5 x squared minus 170 x 280 is (x 7). what are all the roots of the function? use the remainder theorem.

Sagot :

MrRoyal

The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are 2, 4 and -7

How to determine the roots of the function?

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

Read more about roots at:

https://brainly.com/question/13136492

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