SOLUTION: Hello. I was hoping you could please help me? I need to solve this equation : k^5+4k^4-32k^3=0 Since its highest degree is 5, my teacher said we should get 5 roots, but wh

Question 403541: Hello. I was hoping you could please help me?
I need to solve this equation :
k^5+4k^4-32k^3=0
Since its highest degree is 5, my teacher said we should get 5 roots, but when I tried it, I only got 3 roots, which were: 0, -8, and 4
Can you please show me the correct way to do it? I'm doing it by factoring...
Found 2 solutions by MathLover1, richard1234:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

....your equation will be equal to if or
so,
if ...you have three roots, all of them are equal to

if ...here is quadratic, and it has two roots
use quadratic formula to find roots

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
There's a nice theorem (fairly difficult to prove though) called the fundamental theorem of algebra that says that any n-degree polynomial has n complex roots, including multiple roots. Therefore we expect five roots.

Factoring the expression, this becomes

--> or

The first equation has a triple root of 0. The second equation can be factored as --> x = -8, x = 4.
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