In music theory, a musical chord is named according to its roots, or its first root. By knowing the root of a chord, a musician can find the rest of the notes in a chord. How are the roots of chords similar to roots of polynomial functions?

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Mathematics

2 May, 12:03

In music theory, a musical chord is named according to its roots, or its first root. By knowing the root of a chord, a musician can find the rest of the notes in a chord. How are the roots of chords similar to roots of polynomial functions?

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Carissa Hays · Answer 1

A real root of a polynomial function is where the graph crosses the x-axis (also known as a zero or solution). For example, the root of y=x^2 is at x=0.

Roots can also be complex in the form a + bi (where a and b are real numbers and i is the square root of - 1) and not cross the x-axis. Imaginary roots of a quadratic function can be found using the quadratic formula.

A root can tell you multiply things about a graph. For example, if a root is (2,0), then the graph crosses the x-axis at x=2. The complex conjugate root theorem states that if there is one complex root a + bi, then a - bi is also a complex root of the polynomial. So if you are given a quadratic function (must have 2 roots), and one of them is given as complex, then you know the other is also complex and therefore the graph does not cross the x-axis.