Answer:
Solution
roots: (
)
domain X∈3
vertical intercept (0,0)
x = {0, -1.732050808, 1.732050808}
Please, find attached images equation graphs
Explanation:
Simplifying
2x5 + -5x3 + -3x = 0
Reorder the terms:
-3x + -5x3 + 2x5 = 0
Solving
-3x + -5x3 + 2x5 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -5x2 + 2x4) = 0
Factor a trinomial.
x((-1 + -2x2)(3 + -1x2)) = 0
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:
Simplifying
x = 0
Solving
x = 0
Move all terms containing x to the left, all other terms to the right.
Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + -2x2)' equal to zero and attempt to solve:
Simplifying
-1 + -2x2 = 0
Solving
-1 + -2x2 = 0
Move all terms containing x to the left, all other terms to the right.
Add '1' to each side of the equation.
-1 + 1 + -2x2 = 0 + 1
Combine like terms: -1 + 1 = 0
0 + -2x2 = 0 + 1
-2x2 = 0 + 1
Combine like terms: 0 + 1 = 1
-2x2 = 1
Divide each side by '-2'.
x2 = -0.5
Simplifying
x2 = -0.5
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:
Simplifying
3 + -1x2 = 0
Solving
3 + -1x2 = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3
Combine like terms: 0 + -3 = -3
-1x2 = -3
Divide each side by '-1'.
x2 = 3
Simplifying
x2 = 3
Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {0, -1.732050808, 1.732050808}