Exercises

Write the commands to find and display the real roots (avoid decimals unless necessary) of the following using Maple

1. (Give this equation the name eq1)

               eq1 := x^2 → +6*x - 10 = 0
               solve(eq1,x)
           

   Comments: Remember to use the right arrow to exit the superscript.

2. (Give this equation the name eq2)

               eq2 := x^3 → - 4 * x^2 → + x + 6 = 0
               solve(eq2,x)
           

   Comments: Remember to use the right arrow to exit the superscripts.

3. (Give this equation the name eq3)

   Assign the solution to an array called sol

           eq3 := 2x^3 → + 6*x^2 → - 3*x - 34 = 0
           sol := solve(eq3,x)
           

4. (Give this equation the name eq4)

           eq4 := x^4 → + (10/2)*x^3 → - (125/3*x^2 → + 80*x - 36 = 0
           solve(eq4,x)
           

   Comments: Remember to use the right arrow to exit the superscripts and denominators.

5. (Give this equation the name eq5)

           eq5 := a*x^4 → + 5*x^3 → - b*x^2 → + 14*x + c = 0
           solve(eq5,x)
           

   Comments: Notice the * used between a and x^4 and b and x^2; these are required so Maple doesn't see one variable ax or bx. Remember to use the right arrow to exit the superscripts.

6. (Give this equation the name eq6)

           eq6 := x^4 → - exp(x) - 3 = 0
           solve(eq6, x)
           allvalues(%)
           fsolve(eq6,x)
           

   Comments:Remember to use the right arrow → to exit the superscript and divide modes. If solve returns a RootOf partial solution, pass the partial solution to the allvalues command. This is more complicated, but may work to find the symbolic solution (roots). If allvalues also returns a RootOf result, then Maple cannot solve the equation symbolically so you must then use fsolve. If you are just looking for a real root, do not bother with the allvalues command, just use fsolve.