Question

How would I find the zeros of the equation
x^3 - 5x^2 + 6x = 0
?

Answer 1

Factor.

Answer 2

How? Like
x(x^2 - 5x + 6) ?

Answer 3

Yes... that's good. Actually, the other part (x^2 - 5x + 6) could still be factored further ;)

Answer 4

Really? I don't know, I was never good at factoring. How would that work, would you mind trying to explain it?

Answer 5

Crud... I'm not good at explaining how to factor... what two numbers, when multiplied, give 6 and when added, give -5?

Answer 6

-3 and -2, right?

Answer 7

yup.
So.. the factors are...?

Answer 8

x-3 and x-2
try multiplying them ^_^

Answer 9

Ah... this is why I hate factoring...
So it would be like this, right?
x(x^2 - 5x + 6) = 0
x(x-2)(x-3)
?

Answer 10

That's right.
Can you proceed from there?
x(x-2)(x-3) = 0

Answer 11

x = 0, 2, 3
or would it be
x = 0, -2, -3

Answer 12

Why don't you find out?
Plug them in, see which ones work...

Answer 13

Okay, I'll try~

Answer 14

Okay, I'll help you out.
When you have a set of factors that are equal to zero, it suffices for just one of the factors to be zero.
So since you have x(x-2)(x-3) = 0
then just solve
x = 0
x-2 = 0
x-3 = 0

And you'll get your answers ^_^

Answer 15

So it would be 0, 2, and 3 then right?

Answer 16

Well, thanks for your help! It was very helpful so I think I understand better~

Answer 17

No problem ^_^

Answer 18

Would that still work the same if the problem had the first with a power of 4 and not 3?

Answer 19

Well, the factoring would be different, wouldn't it?

Answer 20

Unless all of them have powers increased by 1...