# FROM ROOTS ### Features:

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 (4th 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 x4

• 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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