Question

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

Answer 1

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

Answer 2

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