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Frequently Asked Questions

Which is the best definition of a quadratic form?

Definition of quadratic form. : a homogeneous polynomial (such as x2 + 5xy + y2) of the second degree.

What are quadratic forms over the ring of integers called?

Quadratic forms over the ring of integers are called integral quadratic forms, whereas the corresponding modules are quadratic lattices (sometimes, simply lattices). They play an important role in number theory and topology.

Which is the ellipse of the definite quadratic form?

If the general quadratic form above is equated to 0, the resulting equation is that of an ellipse if the quadratic form is positive or negative-definite, a hyperbola if it is indefinite, and a parabola if c 1 c 2 − c 3 2 = 0. {\displaystyle c_ {1}c_ {2}- {c_ {3}}^ {2}=0.}

What does ± mean in a quadratic equation?

About the Quadratic Formula Plus/Minus. First of all what is that plus/minus thing that looks like ± ? The ± means there are TWO answers: x = −b + √(b 2 − 4ac) 2a. x = −b − √(b 2 − 4ac) 2a. Here is an example with two answers: But it does not always work out like that! Imagine if the curve "just touches" the x-axis.

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