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How to Write a Polynomial Equation of the Least Degree With Roots

A polynomial is a mathematical expression made up of variables, constants, coefficients and exponents. In the polynomial 3x^2 -1, for example, x is the variable, -1 is a constant, 3 is a coefficient and 2 is an exponent. According to the fundamental law of algebra, every polynomial will have as many roots as the number of its largest exponent. The polynomial 3x^2 - 1, therefore, has two roots because its largest, and only, exponent is 2. You use exponents to determine the degree of a polynomial. If the largest exponent in a polynomial is 3, then that polynomial is a third-degree, or cubic, polynomial.

Instructions

- 1
  Write the coefficient of your first term of your polynomial equation. This can be any real number such as 1, 3, 9, -13 or 1.3. For example, write "7."
- 2
  Write the variable of the first term of your equation. Mathematicians conventionally use x as a variable in polynomial equations. For example, write "7x."
- 3
  Write the exponent of the variable you have written. Remember that this is a least-degree equation, so you want the exponent to be as small as possible. Remember also that this equation must have more than one root, so your exponent must be greater than 1. The smallest exponent greater than 1 is 2. For example, write "7x^2."
- 4
  Write an equals (=) sign. For example, write "7x^2 =."
- 5
  Write a zero. For example, "7x^2 = 0." The equation 7x^2 = 0 is a polynomial equation of the least degree with roots.

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