SOLUTION: Find the roots of y=x^3-125. I got down to 5^2-4(1)(25) 25-100 from here I think I'm wrong. Someone please help!

Question 188730This question is from textbook saxon algebra 2
: Find the roots of y=x^3-125.
I got down to 5^2-4(1)(25)
25-100 from here I think I'm wrong.
Someone please help! This question is from textbook saxon algebra 2

Found 2 solutions by josmiceli, jim_thompson5910:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

The roots occur where

(note that )
There is just 1 root, since

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Plug in

Factor the right side using the Difference of Cubes formula. Remember the Difference of Cubes formula is

or Set each factor equal to zero

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Let's solve the first equation :

Start with the given equation.

Add 5 to both sides.

So the first solution is

-----------------------------------------

Now let's solve the second equation

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the next two solutions answers are or

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Answer:

So the three solutions are , or where

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