Question

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.
x = –4, x = –2, or x = 7
x = –7, x = 2, or x = 4
x = –7, x = 5, or x = 280
x = –280, x = –5, or x = 7

Answer 1

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

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that x + 7 is the root of 5x³ + 5x² - 170x + 280, hence:

(5x³ + 5x² - 170x + 280) / (x + 7) = 5x² - 30x - 40

Hence:

(5x³ + 5x² - 170x + 280) = (x + 7)(5x² - 30x - 40)

= 5(x² - 6x - 8)(x + 7)

= 5(x - 4)(x - 2)(x + 7)

The roots are at:

0 = 5(x - 4)(x - 2)(x + 7)

x = 4, x = 2 or x = -7

The roots of 5x³ + 5x² - 170x + 280 are x = 4, x = 2 or x = -7

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