Question

How do you solve `x^2 - 5x+ 6 = 0`?

Answer 1

`color(blue)(x=2 or x=3)`

Explanation:

Given:

`x^2-5x+6=0`

Step.1

Consider

`y = f(x) = x^2-5x+6=0`

Split the middle term of the Quadratic Expression:

`x^2-3x-2x+6=0`

We can rewrite this in factor form:

`x(x-3)-2(x-3) = 0`

Hence,

the factors are: `(x-3) and (x-2)`

This would mean

either `(x-3) = 0 or (x-2) = 0`

Now we can write our solutions as

`color(blue)(x=2 or x=3)`

We can also graph our quadratic to verify our solutions

We analyze the graph and note the following:

x-intercepts are: `(2,0), (3,0)`

Hence, our solutions are verified.

Some additional pieces of useful information for you:

Vertex is at `(2.5, -0.25)`

And,

Axis of Symmetry is at `x = 2.5`