Question

How to find the x-intercept of x² - 2x - 3?

A) Factor the quadratic expression.
B) Use the quadratic formula.
C) Complete the square.
D) Find the discriminant.

Answer 1

The x-intercepts of the quadratic equation x² - 2x - 3 can be found using the quadratic formula, resulting in x-intercepts at x = 3 and x = -1.

Step-by-step explanation:

To find the x-intercept of the quadratic equation x² - 2x - 3, one can use various methods such as factoring, completing the square, using the quadratic formula, or calculating the discriminant. However, the most straightforward way is to use the quadratic formula:

The quadratic formula for an equation of the form ax² + bx + c = 0 is given by x = (-b ± √(b² - 4ac)) / (2a).

For the given quadratic equation x² - 2x - 3, we have:

• a = 1
• b = -2
• c = -3

Plugging these values into the quadratic formula, we get:

x = (2 ± √((-2)² - 4(1)(-3))) / (2 * 1)

x = (2 ± √(4 + 12)) / 2

x = (2 ± √16) / 2

x = (2 ± 4) / 2

Thus, the x-intercepts are x = 3 and x = -1.