The **roots** of the function are found when `y` = 0 (that is, the curve crosses the `x`-axis).

A quadratic may cross the `x`-axis twice, or it may only touch the `x`-axis, or it may not cross the `x`-axis at all. In the first instance, the quadratic will have two roots; in the second instance there will be one root (actually the same root repeated); and in the third instance no *real* roots (the graph does not cross `y` = 0).

The values of `x` when it crosses the `x`-axis are the solutions to the equation.

By drawing a graph, estimate the roots for `y = x^2 - 5x + 6`.

`x` | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 |

`x^2 - 5x + 6` | 12 | 6 | 2 | 0 | 0 | 2 | 6 | 12 |

Answer: `x=2` and `x=3`

With the two roots from the answer, above, show that they are valid roots.

The roots are given where the line crosses the `x`-axis, at (2,0) and (3,0)

When `x=2` or `x=3` then `y=0`

Answer:

Substituting 2 into the function: (2)^{2} - 5(2) + 6 = 4 - 10 + 6 = 0, therefore a root

Substituting 3 into the function: (3)^{2} - 5(3) + 6 = 9 - 15 + 6 = 0, therefore a root

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