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!

Algebra ->  Polynomials-and-rational-expressions -> 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!      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+x%5E3+-+125
The roots occur where y=0
x%5E3+-+125+=+0
x%5E3+=+125
x+=+5 (note that 5%2A5%2A5+=+125)
There is just 1 root, since %28-5%29%2A%28-5%29%2A%28-5%29+=+-125

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E3-125 Start with the given equation.


0=x%5E3-125 Plug in y=0


0=%28x-5%29%28x%5E2%2B5x%2B25%29 Factor the right side using the Difference of Cubes formula. Remember the Difference of Cubes formula is A%5E3+-+B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29



x-5=0 or x%5E2%2B5x%2B25=0 Set each factor equal to zero


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Let's solve the first equation x-5=0:


x-5=0 Start with the given equation.


x=5 Add 5 to both sides.


So the first solution is x=5


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Now let's solve the second equation x%5E2%2B5x%2B25=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=5, and c=25


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%281%29%2825%29+%29%29%2F%282%281%29%29 Plug in a=1, b=5, and c=25


x+=+%28-5+%2B-+sqrt%28+25-4%281%29%2825%29+%29%29%2F%282%281%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25-100+%29%29%2F%282%281%29%29 Multiply 4%281%29%2825%29 to get 100


x+=+%28-5+%2B-+sqrt%28+-75+%29%29%2F%282%281%29%29 Subtract 100 from 25 to get -75


x+=+%28-5+%2B-+sqrt%28+-75+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-5+%2B-+5i%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-5%2B5i%2Asqrt%283%29%29%2F%282%29 or x+=+%28-5-5i%2Asqrt%283%29%29%2F%282%29 Break up the expression.


So the next two solutions answers are x+=+%28-5%2B5i%2Asqrt%283%29%29%2F%282%29 or x+=+%28-5-5i%2Asqrt%283%29%29%2F%282%29


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Answer:

So the three solutions are x=5, x+=+%28-5%2B5i%2Asqrt%283%29%29%2F%282%29 or x+=+%28-5-5i%2Asqrt%283%29%29%2F%282%29 where i=sqrt%28-1%29