Question

Question 21 pts

Find the rational roots of

LaTeX: x^4+8x^3+7x^2-40x-60=0x 4 + 8 x 3 + 7 x 2 − 40 x − 60 = 0

Group of answer choices

-6, -2

-2, 6

2, 6

-6, 2

Answer 1

x = -2 or x = -6 or x = sqrt(5) or x = -sqrt(5)

Explanation:

Solve for x:

x^4 + 8 x^3 + 7 x^2 - 40 x - 60 = 0

The left hand side factors into a product with three terms:

(x + 2) (x + 6) (x^2 - 5) = 0

Split into three equations:

x + 2 = 0 or x + 6 = 0 or x^2 - 5 = 0

Subtract 2 from both sides:

x = -2 or x + 6 = 0 or x^2 - 5 = 0

Subtract 6 from both sides:

x = -2 or x = -6 or x^2 - 5 = 0

Add 5 to both sides:

x = -2 or x = -6 or x^2 = 5

Take the square root of both sides:

Answer: x = -2 or x = -6 or x = sqrt(5) or x = -sqrt(5)