Question

What does it mean when b^2-4ac ≥ 0?

Answer 1

http://en.wikipedia.org/wiki/Quadratic_equation#Discriminant

Answer 2

It means that the solution is Real.

Answer 3

the quadratic equation has real solutions

Answer 4

but I thought b^2-4ac > 0 had two real roots, b^2-4ac = 0, one real root and b^2-4ac < 0 had no real roots

Answer 5

so greater than or equal to zero means there's one real root?

Answer 6

b^2-4ac > 0 had two real roots, b^2-4ac = 0, one real root and b^2-4ac < 0 had no real roots

Answer 7

It means that it has at least one real root.

Answer 8

A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots. There are three cases:

For quadratic equations with integer coefficients, if the discriminant is a perfect square, then the roots are rational numbers—in other cases they may be quadratic irrationals.

If the discriminant is positive, then there are two distinct roots, both of which are real numbers:

If the discriminant is zero, then there is exactly one distinct real root, sometimes called a double root

If the discriminant is negative, then there are no real roots. Rather, there are two distinct (non-real) complex roots, which are complex conjugates of each other:

Answer 9

ohhh... i see. So how would you would if k ≥ - 5?

Answer 10

2x^2 - 8x + 3--5

2x^2 - 8x + 8
2(x-2)(x-2)=0
x=2
the results exactly one distinct real root,
then the discriminant is 0
b^2-4ac =0

Answer 11

ohh, okay. thank you!