Genius Maker - School software - Maths softwareSOFTWARE FOR SOLVINGPOLYNOMIAL EQUATIONS |
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.
- 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 = -5Hence 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 = 5Hence 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 = 2Hence 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 x^{4} - 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 x^{4} + 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).
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