Answer:
x = 1, 3
Explanation:
x² - 4x + 3 = 0 ← quadratic equation in standard form
consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (- 4)
the factors are - 1 and - 3 , since
- 1 × - 3 = + 3 and - 1 - 3 = - 4
use these factors to split the x- term
x² - x - 3x + 3 = 0 ( factor the first/second and third/fourth terms )
x(x - 1) - 3(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ( add 1 to both sides )
x = 1
x - 3 = 0 ( add 3 to both sides )
x = 3
the roots of the equation are x = 1 , 3