Working with polynomials is a common theme on number sense tests. A couple of weeks ago we looked at finding the roots (solutions) of a polynomial with SolveX and SolveXExpo. Today we will look at finding the product of the roots (without having to find the roots themselves). This concept appeared 9 times this year, with a median placement at question # 42.
Number Dojo Level: 302
To master this concept, we first have to understand what is meant by the degree of the polynomial. This refers to the highest power of the variable. For example:
Degree of 2:
- For a polynomial (of degree 2) written as:
- For a polynomial (of degree 3) written as:
- For a polynomial (of degree 4) written as:
- For any polynomial with an even-powered degree (2, 4, etc.), the product of the roots is equal to the constant divided by the highest-powered coefficient.
- For any polynomial with an odd-powered degree (1, 3, etc.), the product of the roots is equal to the negative constant divided by the highest-powered coefficient.