Question

What is the discriminant, and what are the three possible outcomes?

Answer 1

are you familiar with the quadratic formula ?

Answer 2

In which context?

Answer 3

there are other contexts?

Answer 4

assuming they mean the discriminant in the context of quadratic equations
\[\Delta = b^2-4ac\]
this is from the quadratic formula:
\[x= \frac{ -b \pm \sqrt{b^2-4ac}}{2a}\]

since we are taking a square root, sign of the number inside the root will affect the nature of the roots:

if
\[\Delta < 0\]
we have complex roots
if
\[\Delta >0 \]
we have distince real roots

if
\[\Delta = 0\] we have a repeated real root.

Answer 5

Oh yes. Like in analytic geometry it means something different.

Answer 6

i think higher degree polynomials also have discriminants (i know cubics do)

Answer 7

@popjump

see attachment for visual association of discriminant values and the nature of the roots.

Answer 8

Thank you for those responses.