Question

What are the solutions to the quadratic equation 4x² - 9x - 9?

a) x = 3, x = -3/4
b) x = -3, x = 3/4
c) x = 9/4, x = -9/4
d) x = -9/4, x = 9/4

Answer 1

The solutions to the quadratic equation 4x² - 9x - 9 are found using the quadratic formula, resulting in two solutions: x = 3 and x = -3/4.

Step-by-step explanation:

The quadratic equation in question is 4x² - 9x - 9. To find its solutions, we use the quadratic formula -b ± √b² - 4ac over 2a, where a, b, and c are coefficients from the equation ax² + bx + c = 0. In our case, a = 4, b = -9, and c = -9. Plugging these into the quadratic formula, we get:

x = (-(-9) ± √ ((-9) ² - 4(4) (-9))) / (2(4))

x = (9 ± √ (81 + 144)) / 8

x = (9 ± √225) / 8

x = (9 ± 15) / 8

The two solutions are x = 3 when using the ± as a plus and x = -3/4 when using the ± as a minus. Therefore, the correct answer to the student's problem is option a) x = 3, x = -3/4.