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

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

Step-by-step 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:

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

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18