Question

explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?

Answer 1

1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.

2. We can always expect two roots, either identical or different.

1) There are some ways to solve a quadratic equation. We can solve it using the Quadratic Formula, Graphing it or via Newton's Identities, or even factoring

The most common way is via Quadratic Formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}`

Which a, b, and c are the coefficients of a Quadratic Equation, say:

x²+6x+9, a= 1, b=6, and c=9.

`x=\frac{-6\pm\sqrt[]{6^2-4(1)(9)}}{2(1)}=x_1=x_2=-3`

Note that in this case, both roots were equal to -3

2) We can always expect two roots. When the Quadratic Formula yields just one answer then we can call it double root, or 1 root with multiplicity 2, actually there are two roots with the same value.

3) Thus the answer is:

1. There are several ways to solve (Quadratic Formula, Graphing, Newton's Identities, Factoring) the most common is using the Quadratic Formula.

2. We can always expect two roots, either identical or different.