__Solving Quadratic Equations with Maple__

First we use the well known solution formula of the equation

`> `
**x1 := -p/2 + sqrt((p/2)^2 -q);**

`> `
**x2 := -p/2 - sqrt((p/2)^2 -q);**

Now we test it with numerical values:

`> `
**p:=1: q:=-6:**

`> `
**x1;**

`> `
**simplify(%);**

`> `
**simplify(x2);**

Next we use the formula with algebraic expressions:

`> `
**p := 5*a-1: q := 6*a^2-a-2: **

`> `
**x1;**

`> `
**simplify(%);**

To further simplify this expression, we need additional information about a, e.g.

`> `
**assume(a>=3);**

`> `
**simplify(x1);**

`> `
**simplify(x2);**

What happens in the other case?

`> `
**assume(a<3);**

`> `
**simplify(x1);**

`> `
**simplify(x2);**

Of course Maple can solve quadratic equations itself:

`> `
**restart;**

`> `
**QE := x^2+p*x+q:**

`> `
**solve(QE, x);**

`> `
**p :=1:q:=-6:**

`> `
**solve(QE, x);**

`> `
**p := 5*a-1: q := 6*a^2-a-2: **

`> `
**solve(QE, x);**