For a polynomial with real coefficients, complex roots come in conjugate pairs, that is: if and only if .
Roots and Coefficients
Let , , , and be the roots of the following polynomials (as necessary according to the degree of each). The following relationships are known as Vieta's formulae.
For a quadratic:
For a cubic:
For a quartic:
Using Substitutions
If an equation in has a root , a substitution can be applied, giving a resulting equation in having a root .
Example
The equation has roots and . Find a quadratic equation with roots and .