# How do you find the zeros, real and imaginary, of y= 3x^2+4x+2  using the quadratic formula?

Dec 21, 2015

Substitute the coefficients into the equation and evaluate.

#### Explanation:

The quadratic equation is $x = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c \setminus}}{2 a}$
In the example a = 3, b = 4 and c = 2

$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \cdot 3 \cdot 2}}{2 \cdot 3}$
$x = \frac{- 4 \pm \sqrt{16 - 24}}{6}$
$x = - \frac{4}{6} \pm \frac{\sqrt{- 8}}{6}$
$x = - \frac{2}{3} \left(1 + \sqrt{- 2}\right)$ or $- \frac{2}{3} \left(1 - \sqrt{- 2}\right)$

The equation only has imaginary roots. The graph never touches or crosses the x axis.