X^2-4x+3=0 determine the nature of the roots​

Step 1: Factor left side of equation.

Step 2: Set factors equal to 0.

x^2 - 4x + 3 = 0

Factor the left side.

What two numbers when multiplied yield 3 but when added yield the middle coefficient -4?

How about -1 time -3?

Yes, (-1)(-3) is 3 but when added yield -4.

(x - 3)(x - 1) = 0

Set each factor to 0 and solve for x.

x - 3 = 0

x = 3

x - 1 = 0

x = 1

The word root is just another word for solution or the zero of a polynomial.

x = 1 or x = 3 are the roots.