How do you find the roots, real and imaginary, of y=12x^2 -7x -12  using the quadratic formula?

May 10, 2018

Your roots are $x = - \frac{3}{4}$ or $1 \frac{1}{3}$

Explanation:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

By inputting values, we're given:

$x = \frac{- \left(- 7\right) \pm \sqrt{{7}^{2} - \left(4 \cdot 12 \cdot - 12\right)}}{2 \cdot 12}$

$x = \frac{7 \pm \sqrt{49 + 576}}{24}$

$x = \frac{7 \pm \sqrt{625}}{24}$

$x = \frac{7 \pm 25}{24}$

$x = \frac{7 + 25}{24} = \frac{32}{24} = 1 \frac{1}{3}$

$x = \frac{7 - 25}{24} = - \frac{18}{24} = - \frac{3}{4}$

Your roots are $x = - \frac{3}{4}$ or $1 \frac{1}{3}$