# Thread: Finding the co-ords where y = 0..

1. ## Finding the co-ords where y = 0..

$y = x^{1/3} - x^2$

How do I solve this equation to find the roots. It's not a quadratic equation because it involves cubic root of x.

2. Hi there!

Originally Posted by struck
$y = x^{1/3} - x^2$

How do I solve this equation to find the roots. It's not a quadratic equation because it involves cubic root of x.
I would try:

$0 = x^{1/3} - x^2$

$x^2 = x^{1/3}$

next step: (both sides)^3

$(x^2)^3 = x^1$

$x^6 = x^1$

$0 = x^6 - x^1$

$0 = x (x^5 - 1)$

=> x = 0 or x=1 (solving $x^5 = 1$ leads to x = 1)

3. Originally Posted by struck
$y = x^{1/3} - x^2$

How do I solve this equation to find the roots.
$0 = x^{\frac{1}{3}} - x^2$

$0 = x^{\frac{1}{3}}\left(1 - x^{\frac{5}{3}}\right)$

$x^{\frac{1}{3}} = 0$ ... $x = 0$

$x^{\frac{5}{3}} = 1$ ... $x = 1$