Find the zeros of f (x) = x squared-x

F (x) = x² - x

x² - x = 0

x² - x + 0 = 0

x = - (-1) + / - √ ((-1) ² - 4 (1) (0))

2 (1)

x = 1 + / - √ (1 - 0)

2

x = 1 + / - √ (1)

2

x = 1 + / - 1

2

x = ¹/₂ + ¹/₂

x = ¹/₂ + ¹/₂ x = ¹/₂ - ¹/₂

x = 1 x = 0

We need solve:

x² - x = 0

One simple answer is: x = 0.

Just try it:

0² - 0 = 0 < - - - This is a correct statement.

So we already have one answer: x = 0.

Since we have a ² there, we're looking for two answers.

Now, let's divide our function by x.

We then get:

x² / x = x

x / x = 1

0 / x = 0

So

x - 1 = 0

For this, the solution is x = 1.

So there we have two answers:

x = 0

x = 1