# How do you find the roots, real and imaginary, of y=12x^2 - 42x + 18  using the quadratic formula?

Mar 22, 2016

1/2 and 3

#### Explanation:

$y = 12 {x}^{2} - 42 x + 18 = 0.$
$D = {d}^{2} = {b}^{2} - 4 a c = 1764 - 864 = 900$ --> $d = \pm 30$
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{42}{24} \pm \frac{30}{24} = \frac{7}{4} \pm \frac{5}{4}$
$x = \frac{12}{4} = 3 \mathmr{and} x = \frac{2}{4} = \frac{1}{2}$