Find the Roots of a Standard Form Quadratic: x² - 2x - 3

To solve this quadratic equation $x^2 - 2x - 3 = 0$, we will employ the quadratic formula.

• Step 1: Identify the coefficients: $a = 1$, $b = -2$, and $c = -3$.
• Step 2: Calculate the discriminant $\Delta = b^2 - 4ac$.
• Step 3: Substitute into the quadratic formula to find the roots.

Now, let's work through each step:

Step 1: The coefficients are $a = 1$, $b = -2$, $c = -3$.

Step 2: Calculate the discriminant:
$\Delta = (-2)^2 - 4 \times 1 \times (-3) = 4 + 12 = 16$.

Step 3: Substitute into the quadratic formula:
$x = \frac{-(-2) \pm \sqrt{16}}{2 \times 1} = \frac{2 \pm 4}{2}$.

This gives us two solutions:

• For the '+' sign: $x_1 = \frac{2 + 4}{2} = \frac{6}{2} = 3$.
• For the '-' sign: $x_2 = \frac{2 - 4}{2} = \frac{-2}{2} = -1$.

Therefore, the solutions to the equation $x^2 - 2x - 3 = 0$ are $x_1 = 3$ and $x_2 = -1$, which corresponds to choice 2.