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. You can also use the right click to assign the equation to a name, solve the equation or both.

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)
           

   Comments: You can also use the right click menu to do this problem (see exercise 7)

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. You can also use the right click to assign the equation to a name, solve the equation or both.

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. You can also use the right click to assign the equation to a name, solve the equation or both. However, in this case you have to use Solve equation for a variable->x so Maple knows to solve for x rather than a, b, or c.

6. (Give this equation the name eq6)

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

   Comments:Remember to use the right arrow → to exit the superscript and divide modes. You can also use the right click to assign the equation to a name, solve the equation or both. However, in this case you have to use Solve numerically or fsolve to obtain an approximation of the single real solution. 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 you are just looking for a real root, do not bother with the allvalues command, just use fsolve.

7. (Give this equation the name eq3)

   Isolate the solutions and assign them the names sol[1], sol[2] and sol[3].

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

   1. Right-click on list of solutions: select element->1)
   2. Right-click resulting solution: Assign to a Name)
   3. In window that opens type: sol[1])
   4. Right-click on original list of solutions: select element->2)
   5. Right-click resulting solution: Assign to a Name)
   6. In window that opens type: sol[2])
   7. Right-click on original list of solutions: select element->3)
   8. Right-click resulting solution: Assign to a Name)
   9. (In window that opens type: sol[3])

   Comments: Remember to use the right arrow to exit the superscripts. You can also use the right click to assign the equation to a name, solve the equation or both. Notice that Maple changes sol[1], sol[2], and sol[3] to subscripts.