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);