Genius Maker - School software - Maths softwareFORM POLYNOMIAL EQUATIONSFROM ROOTS |
The Polynomial Formation is a mathematics educational software, which facilitates to find the polynomial equations from the roots. It can form polynomial equations upto fourth order. ( ie., Quartic Equations). Also this software supports for complex number roots as well as for complex numbers in the formed equations.
- Open Genius Maker software and click "Polynomial Formation" button. It opens the Polynomial Formation window.
- You may see 2 menus, the first one for entering the values of roots (input) and the second one displays the resulting equation (output).
Example - 1
- Find the polynomial equation, whose roots are 1, -3 and 5.
Enter the values 1, -3 and 5 in the first 3 boxes in the input field. Leave the fourth box as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x³ - 3 x² - 13 x + 15 = 0
This is the required polynomial equation with roots as 1, -3 and 5.
Example - 2
- Find the quadratic equation, whose roots are 4 and -5.
Click "Clear Data" button.
- Enter the values 4, and -5 in the first 2 boxes in the input field. Leave third and fourth box as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x² + 1 x - 20 = 0
This is the required quadratic equation with roots as 4 and -5.
Example - 3
- Find the resulting cubic equation, x (x+1) (x-7) = 0
Here the roots are x = 0, x = -1 and x = 7.
- Click "Clear Data" button.
- Enter the values 0, -1 and 7 in the first 3 boxes in the input field. Leave fourth box as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x³ - 6 x² - 7 x + 0 = 0
This is the required cubic equation which results from (x+1) (x-7) (x) = 0.
Example - 4
- Find the quartic (4^{th} order) polynomial equation, whose roots are 2, 8, -7 and -1.
Enter the values 1, -3 and 5 in the first 3 boxes in the input field. Leave the fourth box as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x^4 - 2 x³ - 57 x² + 58 x + 112 = 0
Here X^4 means x^{4}
This is the required quartic polynomial equation with roots as 2, 8, -7 and -1.
Example - 5
- Find the quadratic equation, whose roots are (4 + 3i) and (4 - 3i)
Click "Clear Data" button.
- Click "Complex Number ON / OFF" button. You can see the complex number fields appearing in the menu.
- Enter the value 4 in the real number field of first x value
- Enter the value 3 in the complex number field of first x value
- Enter the value 4 in the real number field of second x value
- Enter the value -3 in the complex number field of second x value
- Leave third and fourth boxes of both real and complex fields as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x² - 8 x + 25 = 0
This is the required quadratic equation with roots as (4 + 3i) and (4 - 3i).
Example - 6
- Find the cubic equation, whose roots are 3, (2 + i) and (2 - i)
Click "Clear Data" button.
- If complex number fields are not visible, click "Complex Number ON / OFF" button. You can see the complex number fields appearing in the menu.
- Enter the value 3 in the real number field of first x value
- Leave the complex number field of first x value as blank
- Enter the value 2 in the real number field of second x value
- Enter the value 1 in the complex number field of second x value
- Enter the value 2 in the real number field of third x value
- Enter the value -1 in the complex number field of third x value
- Leave fourth boxes of both real and complex fields as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x³ - 7 x² + 17 x - 15 = 0
This is the required cubic equation with roots as 3, (2 + i) and (2 - i).
Example - 7
- Find the cubic equation, whose roots are (2 + 3i), (1 + 4i) and (4 - 6i)
Click "Clear Data" button.
- If complex number fields are not visible, click "Complex Number ON / OFF" button. You can see the complex number fields appearing in the menu.
- Enter the value 2 in the real number field of first x value
- Enter the value 3 in the complex number field of first x value
- Enter the value 1 in the real number field of second x value
- Enter the value 4 in the complex number field of second x value
- Enter the value 4 in the real number field of third x value
- Enter the value -6 in the complex number field of third x value
- Leave fourth boxes of both real and complex fields as blank.
- Click "Find Polynomial equation" button.
- You can see the result appearing in the second menu as shown below.
x³ - (7+1i) x² + (44+21i) x - (26+104i) = 0
This is the required cubic equation with roots as 3, (2 + i) and (2 - i). You may note that the software is capable of producing equations, even if the resulting polynomial equation contains complex numbers.
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