The image you uploaded contains the quadratic function $x^2 - 4x + 3 = 0$, and the quadratic formula for finding the roots of the equation is provided:

$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this equation, the coefficients from $x^2 - 4x + 3 = 0$ are:

• $a = 1$
• $b = -4$
• $c = 3$

Let's plug these values into the quadratic formula and solve for $x$.

$x_{1,2} = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(3)}}{2(1)}$ $x_{1,2} = \frac{4 \pm \sqrt{16 - 12}}{2}$ $x_{1,2} = \frac{4 \pm \sqrt{4}}{2}$ $x_{1,2} = \frac{4 \pm 2}{2}$

Now, calculate the two possible values for $x$:

1. $x_1 = \frac{4 + 2}{2} = 3$
2. $x_2 = \frac{4 - 2}{2} = 1$

Thus, the solutions to the quadratic equation $x^2 - 4x + 3 = 0$ are $x = 3$ and $x = 1$.

Would you like more details or have any further questions?

Here are five related questions to consider:

1. How does the discriminant ($b^2 - 4ac$) affect the nature of the roots?
2. Can the quadratic formula be used for non-real solutions?
3. How can you factor the equation $x^2 - 4x + 3 = 0$ without using the quadratic formula?
4. What are the graphical implications of the roots of a quadratic function?
5. How does completing the square compare to using the quadratic formula for solving equations?

Tip: The discriminant $b^2 - 4ac$ tells you whether the roots are real and distinct, real and equal, or complex.