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

2 Answers
Shreya
Mar 22, 2018

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.

Nghi N
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 = -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).

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