Question

How do you solve `0=2x^2 + 5x - 12` using the quadratic formula?

Answer 1

`x_(1,2) = (-5 +- 11)/4`

Explanation:

For a general form quadratic equation

`color(blue)(ax^2 + bx + c = 0)`

its roots can be determined using the quadratic formula

`color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4 * a * c))/(2 * a))`

In your case, you have

`2x^2 + 5x - 12 = 0`

which implies that `a = 2`, `b = 5`, and `c = -12`.

The two roots will thus take the form

`x_(1, 2) = (-5 +- sqrt(5^2 - 4 * 2 * (-12)))/(2 * 2)`

`x_(1,2) = (-5 +- sqrt(121))/4`

`x_(1,2) = (-5 +- 11)/4 = {(x_1. = (_5 - 11)/4 = -4), (x_2 = (-5 + 11)/4 = 3/2) :}`

The two solutions to this quadratic equation will thus be

`x_1 = color(green)(-16)" "` and `" "x_2 = color(green)(3/2)`