discriminant signs (1 Viewer)

[abdog]

I understand b^2-4ac = 0 for equal roots and <0 for no roots. But I get confused when < or equal and > or equal comes out. Does anyone have a list of the discriminant signs?

 

[Nws m8]

Less than zero means complex roots (in 4u you can define them by i, but for 2/3u, you just go "undefined")
Greater tHan zero means real roots

 

[D94]

No real roots for < 0.

Think about it, if you apply the quadratic formula, for < 0, you will have a negative number under the square root sign, so you will get an imaginary result.

When it's > 0, the square root will yield a real result.

When it's = 0, then square root will be zero - so you will get x = -b/2a which is just equal roots.

 

[abdog]

Yeah I get that. But what I don't get is when should we put the ">/< or equal to" sign?

 

[Come at me]

No real roots for < 0.

Think about it, if you apply the quadratic formula, for < 0, you will have a negative number under the square root sign, so you will get an imaginary result.

When it's > 0, the square root will yield a real result.

When it's = 0, then square root will be zero - so you will get x = -b/2a which is just equal roots.

That's what "Nws m8" said lol

 

[D94]

Yeah I get that. But what I don't get is when should we put the ">/< or equal to" sign?

A discriminant is a number, so it can only be negative, zero or positive. When you find a number which is satisfies the "equal to" condition in "greater/less than or equal to" which isn't the number zero, please let me know.

I guess if it had an unknown, such as the discriminant is 5k² + 10, then you could say D = 5k² + 10 >= 10 because k² is always >= 0, but that's because you have an unknown, although unless the task was to find that case, you will be given conditions which help you to solve the discriminant.

 

[abdog]

No, I mean, these signs, ≥ or ≤, when do we use them?

 

[D94]

No, I mean, these signs, ≥ or ≤, when do we use them?

Ok, adding to what I wrote before...

If the question tells you it has 2 real roots, then you should use ≥ because it could be 2 equal roots or 2 distinct real roots; or if it says the function has at least 1 root, or something which indicates the function will cut the axis at some point. If the question tells you the function is never negative, you should use ≤ because it is either completely above the axis (by taking the '<' case) or sitting on the axis (the '=' case).

 

[Hypem]

Discriminant ≥ 0, then real roots.
Discriminant > 0, then real, distinct roots.
Discriminant = 0, then 2 real equal roots, or 1 real root.
Discriminant < 0, then no real roots.

≤ 0 isn't really used.