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

Question

Genesis Allen · Accepted Answer

see below

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.

Julia Adams · Answer

Meaning of the Discriminant D

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).