Study Guidance: Solving Quadratic Equations (Equação do 2° Grau)

Q1. Solve the quadratic equation:

$x^2 - 5x + 6 = 0$

Background

Topic: Quadratic Equations (Equações do 2° Grau)

This question tests your ability to solve a quadratic equation, which is a polynomial equation of degree 2. The standard form is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Key Terms and Formulas

• Quadratic Formula:

  $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

• Discriminant: $\Delta = b^2 - 4ac$

• Factoring: Sometimes, quadratics can be factored as $(x - r_1)(x - r_2) = 0$ where $r_1$ and $r_2$ are the roots.

Step-by-Step Guidance

1. Identify the coefficients: $a = 1$, $b = -5$, $c = 6$.

2. Calculate the discriminant using $\Delta = b^2 - 4ac$.

3. Substitute the values of $a$, $b$, and $c$ into the discriminant formula and simplify.

4. Set up the quadratic formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$ using your calculated discriminant.

5. At this point, you are ready to substitute the values and solve for $x$. Try to complete the calculation yourself!

Try solving on your own before revealing the answer!

Final Answer: $x = 2$ and $x = 3$

Using the quadratic formula or factoring, the equation $x^2 - 5x + 6 = 0$ factors as $(x - 2)(x - 3) = 0$, so the solutions are $x = 2$ and $x = 3$.