Genius Maker - School software - Maths software SOFTWARE FOR SOLVING  POLYNOMIAL EQUATIONS

Features of Roots of Polynomial Equations Software:

The Roots of Polynomial Equations is a mathematics educational software, which facilitates to solve (find all the roots of) a given polynomial equation. It can find roots of polynomial equations upto fourth order. (ie., Quartic Equations). This software can find both real and complex number roots. 

How to start with Roots of Polynomial equations software ?

• Open Genius Maker software and click "Roots of Polynomial" button. It opens the Roots of Polynomial window.
• You may see 2 menus, the first one for selecting the order of polynomial and the second one display of input and output fields.

Example - 1

• Find the roots of the quadratic equation x² + 3 x - 10 = 0

  • Click "Clear Data" button.

  • Select the second option, "Quadratic equation" from the top menu.

  • The title of the second menu should read as "Quadratic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x² + B x + C = 0

  • In the current problem, A = 1, B = 3 and C = -10.

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    Two Real roots 
    x = 2
    x = -5

  • Hence the roots of the given quadratic equation are 2 and -5.

Example - 2

• Find the roots of the quadratic equation x² - 6 x + 13 = 0

  • Click "Clear Data" button.

  • Select the second option, "Quadratic equation" from the top menu.

  • The title of the second menu should read as "Quadratic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x² + B x + C = 0

  • In the current problem, A = 1, B = -6 and C = 13.

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    Two Imaginary roots 
    x = ( 3 + 2 i )
    x = ( 3 - 2 i )

  • Hence the roots of the given quadratic equation are (3 + 2i) and  (3 - 2i) .

Example - 3

• Find the roots of the cubic equation x² - 10 x + 25 = 0

  • Click "Clear Data" button.

  • Select the second option, "Quadratic equation" from the top menu.

  • The title of the second menu should read as "Quadratic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x² + B x + C = 0

  • In the current problem, A = 1, B = -10 and C = 25.

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    Two Real roots, which are equal
    x = 5
    x = 5

  • Hence the 2 roots of the given quadratic equation are same and are equal to 5 .

Example - 4

• Find the roots of the cubic equation x³ - 3 x² - 4 x + 12 = 0

  • Click "Clear Data" button.

  • Select the third option, "Cubic equation" from the top menu.

  • The title of the second menu should read as "Cubic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x³ + B x² + C x + D = 0

  • In the current problem, A = 1, B = -3, C = -4 and D = 12

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    Three real roots 
    x = 3
    x = -2
    x = 2

  • Hence the roots of the given cubic equation are 3, -2 and 2.

Example - 5

• Find the roots of the cubic equation x³ - 14 x² + 69 x - 116 = 0

  • Click "Clear Data" button.

  • Select the third option, "Cubic equation" from the top menu.

  • The title of the second menu should read as "Cubic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x³ + B x² + C x + D = 0

  • In the current problem, A = 1, B = -14, C = 69 and D = -116

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    One Real root and Two Imaginary roots 
    x = 4
    x = ( 5 + 2 i )
    x = ( 5 - 2 i )

  • Hence the roots of the given cubic equation are 4, (5 + 2i) and (5 - 2i).

Example - 6

• Find the roots of the polynomial quartic equation x⁴ - 3 x³ + 40 x² - 26 x - 600 = 0

  • Click "Clear Data" button.

  • Select the fourth option, "Quartic equation" from the top menu.

  • The title of the second menu should read as "Quartic equation"
  • Now you can enter the values of co-efficient in the equation.

  • You may note the format displayed for input. In this case, it reads as

     A x⁴ + B x³ + C x² + D x + E = 0

  • In the current problem, A = 1, B = -3, C = 40, D = -26 and E = -600

  • Enter the values in the input boxes accordingly.
  • Click "Find All Roots" button.
  • You can see the result appearing as shown below.

    Two Real roots and Two Imaginary roots 
    x = 4 
    x = -3 
    x = ( 1 + 7 i )
    x = ( 1 - 7 i )

  • Hence the roots of the given Quartic equation are 4, 3, (1 + 7i) and (1 - 7i).