# Determine the roots of the equation x^2-5x+6=0.

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### 2 Answers

We'll apply the quadratic formula

The original equation is: x^2-5x+6=0

x1 = [-b + sqrt(b^2 - 4ac)]/2a

We'll identify the coefficients:

a = 1

b = -5

c = 6

b^2 - 4ac = (-5)^2 - 4*1*6 = 25 - 24

sqrt(b^2 - 4ac) = sqrt(25 - 24)

sqrt(b^2 - 4ac) = 1

We'll substitute in the formula:

x1 = [-(-5) + sqrt(25 - 24)]/2

x1 = (5+1)/2

x1 = 3

x2 = (5-1)/2

x2 = 2

**The roots of the equation are {2 ; 3}.**

x^2 - 5x + 6 = 0

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

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

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

Therefor roots x1 and x2 of equation are:

x1 = 3 and

x2 = 2