For an equation with roots defined by the quadratic x^2 - 4x + 3, what is the sum of the roots?

To find the sum of the roots of a quadratic equation in the form ( ax^2 + bx + c ), you can use Vieta's formulas, which state that the sum of the roots is equal to ( -\frac{b}{a} ), where ( b ) is the coefficient of ( x ) and ( a ) is the coefficient of ( x^2 ).

For the given quadratic equation ( x^2 - 4x + 3 ):

• The coefficient ( a ) is 1 (from ( x^2 )),

• The coefficient ( b ) is -4 (from the term (-4x)).

Using Vieta's formula to calculate the sum of the roots:

[

\text{Sum of the roots} = -\frac{b}{a} = -\frac{-4}{1} = 4

]

Thus, the sum of the roots for the equation ( x^2 - 4x + 3 ) is 4, which confirms that the correct response is indeed the second choice.