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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 times -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.
Answer: x = 1 or x = 3 are the roots.