# What is the discriminant of f(x)=-3x^2-2x-1?

Sep 11, 2014

Please see the following link to learn how to find the discriminant.

Aug 2, 2015

The discriminant is $- 8$

#### Explanation:

$f \left(x\right) = - 3 {x}^{2} - 2 x - 1$ is of the form $a {x}^{2} + b x + c$,

with $a = - 3$, $b = - 2$ and $c = - 1$

The discriminant $\Delta$ is given by the formula:

$\Delta = {b}^{2} - 4 a c$

$= {\left(- 2\right)}^{2} - \left(4 \times - 3 \times - 1\right) = 4 - 12 = - 8$

The discriminant is the expression under the square root in the quadratic formula for the solutions of $a {x}^{2} + b x + c = 0$, viz

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

In our case $\Delta = - 8 < 0$, so the square root has a pure imaginary value and the solutions of $f \left(x\right) = 0$ are complex conjugates.