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Derivation of Quadratic Formula

The name Quadratic comes from "quad" meaning square, because the variable gets squared like x 2. It is also called an "Equation mathematics quadratic equations pdf result Degree 2" because of the "2" on the x. Play with the " 1 piece nature wooden watch 90 Equation Explorer " so you can see:.

It is called the Discriminantbecause it can "discriminate" between the possible types of answer:. Complex solutions? Let's talk about them after we see how to use the formula. It was all over at 2 am. It means our answer will include Imaginary Numbers. Hide Ads About Ads. Quadratic Equations An example of a Quadratic Equation : Quadratic Equations make nice curves, like this one: Name The name Quadratic comes from "quad" meaning square, because the variable gets squared like x 2.

The " solutions " to the Quadratic Equation are where it is equal to zero. They are also called " roots ", or sometimes " zeros ". We can Factor the Quadratic find what to multiply to make the Quadratic Equation. Or we can use the special Quadratic Formula : Just plug in the values of a, b and c, and do the calculations. We will look at this method in more detail. Hard Questions: 1 2 3 4 5 6 7 8. This one is a little more tricky: Where is a?

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On the other hand, it is an open problem whether every finite group is the Galois group of a field extension of the field Q of the rational numbers. For example, in his commentary, Liouville completely missed the group-theoretic core of Galois' method. As long as one does not also specify the ground field , the problem is not very difficult, and all finite groups do occur as Galois groups. Galois introduced the subject for studying roots of polynomials. See the article on Galois groups for further explanation and examples. Galois' theory was notoriously difficult for his contemporaries to understand, especially to the level where they could expand on it. Outside France, Galois' theory remained more obscure for a longer period.
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