Question

Given the equation y = 2x² - 5x - 3, find the x-intercepts.

a) x = 3, -1/2
b) x = 1, -3
c) x = -3, 1/2
d) x = -1, 3

Answer 1

The x-intercepts of the equation y = 2x² - 5x - 3 are found using the quadratic formula, resulting in the x-intercepts being x = 3 and x = -1/2.

Step-by-step explanation:

To find the x-intercepts of the equation y = 2x² - 5x - 3, we need to set y to zero and solve the resulting quadratic equation. We can do this by applying the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), where in our equation, a = 2, b = -5, and c = -3.

Plugging in these values, we get:

x = (-(-5) ± √((-5)² - 4 * 2 * (-3))) / (2 * 2)

x = (5 ± √(25 + 24)) / 4

x = (5 ± √49) / 4

x = (5 ± 7) / 4

So, the two solutions for x are:

x = (5 + 7) / 4 = 12 / 4 = 3

x = (5 - 7) / 4 = -2 / 4 = -1/2

Therefore, the x-intercepts of the equation are x = 3 and x = -1/2, which corresponds to option a.