Find the Roots (Zeros) 2x^4-5x^3+53x^2-125x+75=0

Math
Factor the left side of the equation.
Tap for more steps…
Regroup terms.
Factor out of .
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Let . Substitute for all occurrences of .
Factor by grouping.
Tap for more steps…
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps…
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Tap for more steps…
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Factor out of .
Tap for more steps…
Factor out of .
Factor out of .
Factor out of .
Let . Substitute for all occurrences of .
Factor by grouping.
Tap for more steps…
Reorder terms.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Tap for more steps…
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Tap for more steps…
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Factor.
Tap for more steps…
Replace all occurrences of with .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Tap for more steps…
Set the first factor equal to .
Subtract from both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
Rewrite as .
Rewrite as .
Rewrite as .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Move to the left of .
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps…
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set the next factor equal to and solve.
Tap for more steps…
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Tap for more steps…
Set the next factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Tap for more steps…
Divide each term in by .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
The final solution is all the values that make true.
Find the Roots (Zeros) 2x^4-5x^3+53x^2-125x+75=0

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top