Question

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

Answer 1

see below

Explanation:

We know,for an equation of the form, `ax^2+bx+c=0`
the discriminant `D` is equal to `sqrt(b^2-4ac)`.
Thus,comparing the given equation with the standard form, we get `D` as `sqrt({3}^2-4xx{-20}{-1})` 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.

Answer 2

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 = -b/(2a) +- d/(2a)`
where `d^2 = D` (Discriminant).

In this formula,
`-b/(2a)` represents the x-coordinate of the parabola axis of symmetry.
`+- d/(2a)` 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).