(In algebra,) what the heck is a discriminant? and a (?) i think it's called a quadratic equation?

Question

plz n thnx!
<33
Kassy

Answer 1

discriminant= b²- 4ac

b²- 4ac > 0 => 2 real roots
b²- 4ac < 0 => no real roots or complex roots
b²- 4ac = 0 => 1 root or 2 equal roots

Answer 2

Many equations have a quantity called a discriminant, which characterises the kinds of solutions it can have. Quadratic equations have two solutions, and they can be either both real and distinct, real and repeated, or complex conjugate. The discriminant of the quadratic equation ax^2 + bx + c = 0 is the quantity b^2 - 4ac. If this quantity is positive, you have two real roots. If negative, you have complex conjugate roots. If equal to zero, you have a double (repeated) root. So, the discriminant "discriminates" between the kinds of solutions you can have.

Many other kinds of equations have discriminants as well. For instance, the discriminant of the reduced cubic equation

y^3 - py - q = 0

is

(p^3)/27 - (q^4)/81.

Since every cubic equation can be put into the reduced form, it follows that the discriminant can be used for all cubic equations.

Answer 3

Given a general quadratic equation

ax^2 + bx + c = 0

The general solution is the quadratic formula

x = [- b +- sqrt(b^2 - 4ac)]/2a

and

b^2 - 4ac is the discriminant

if = 0, quadratic has one root (or two equal roots)

if > 0, quadratic has two real roots

if < 0, quadratic has two imaginary roots

Answer 4

The discriminant is part of the quadratic formula.
If you have a quadratic equation of the form ax²+bx+c = 0
then the discriminant is (b²-4ac)
The discriminant tells you when you have real, non-real, or duplicate roots. When the discriminant is negative you have complex roots. When it is zero you have duplicate roots. When it is positive you have two different real roots.