Find the solutions to 2x^5-5x^3-3x=0. what are the x-intercepts of the graph of the function f(x)=2x^5-5x^3-3x?

Solution

roots: ()

domain X∈3

vertical intercept (0,0)

x = {0, -1.732050808, 1.732050808}  

Please, find attached images equation graphs

Step-by-step 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}