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

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Answer 1 · 2018-01-11T00:12:36

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

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

enter image source here

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#