# What is the discriminant of -20x^2+3x-1=0 and what does that mean?

Mar 22, 2018

see below

#### Explanation:

We know,for an equation of the form, $a {x}^{2} + b x + c = 0$
the discriminant $D$ is equal to $\sqrt{{b}^{2} - 4 a c}$.
Thus,comparing the given equation with the standard form, we get $D$ as $\sqrt{{\left\{3\right\}}^{2} - 4 \times \left\{- 20\right\} \left\{- 1\right\}}$ which,on simplifying comes out to be $\sqrt{- 71}$ which is an imaginary number.
Whenever the $D$ becomes less than zero the roots become imaginary.

Mar 22, 2018

Meaning of the Discriminant D

#### Explanation:

To fully understand the meaning of D, you may read the math article, titled :"Solving quadratic equation by the quadratic formula in graphic form", on Socratic Search, or Google.

The improved formula, that gives the 2 values of x, is:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a}$
where ${d}^{2} = D$ (Discriminant).

In this formula,
$- \frac{b}{2 a}$ represents the x-coordinate of the parabola axis of symmetry.
$\pm \frac{d}{2 a}$ represent the 2 distances from the axis of symmetry to the 2 x-intercepts of the parabola
.
In the above example, $D = {d}^{2} = 9 - 80 = - 71$. Then, d is imaginary. There are no x-intercepts. The downward parabola graph doesn't intersect the x-axis. It is completely below the x-axis (a < 0).