SOLUTION: Find the solutions of the equation. x^3 + 6x^2 + 10x = 0

Algebra ->  Square-cubic-other-roots -> SOLUTION: Find the solutions of the equation. x^3 + 6x^2 + 10x = 0      Log On


   

Question 903858: Find the solutions of the equation.
x^3 + 6x^2 + 10x = 0
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+%2B+6x%5E2+%2B+10x+=+0

x%28x%5E2+%2B+6x+%2B+10%29+=+0

x=0 or x%5E2+%2B+6x+%2B+10+=+0

x+=+0 or x+=+3%2Bi or x+=+3-i

Side Note: I solved x%5E2+%2B+6x+%2B+10+=+0 to get x+=+3%2Bi or x+=+3-i. I used the quadratic formula to get that result. Here is a quadratic formula solver. There are tons of other quadratic formula calculators out there on the internet as well.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


x%5E3+%2B+6x%5E2+%2B+10x+=+0 ...factor out x
x%28x%5E2+%2B+6x+%2B+10%29+=+0
one solution is highlight%28x=0%29
the other two you will find if you use quadratic formula to solve %28x%5E2+%2B+6x+%2B+10%29+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A10+%29%29%2F%282%2A1%29+
x+=+%28-6+%2B-+sqrt%28+36-40%29%29%2F2+
x+=+%28-6+%2B-+sqrt%28+-4%29%29%2F2+
x+=+%28-6+%2B-+2i%29%2F2+
x+=+%28-cross%286%293+%2B-+cross%282%29i%29%2Fcross%282%29+
x+=+-3+%2B-+i+
second solution:
highlight%28x+=+-3+%2B+i%29+
third solution:
highlight%28x+=+-3+-+i%29+
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+%2B+6x%5E2+%2B+10x%29+