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Polynomial roots
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A degree \(n\) polynomial has \(n\) roots counting multiplicity, and its roots may be real or complex; for a polynomial with real coefficients, complex roots occur in conjugate pairs, and the sum and product of roots are given by the coefficient relationships \(\frac{-a_{n-1}}{a_n}\) and \(\frac{(-1)^n a_0}{a_n}\).
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Degree n polynomial has n roots
AHL 2.12
A polynomial with degree n has n roots. These roots are not necessarily distinct, and not always real.
Sum and product of roots
AHL 2.12
For a polynomial's roots:
thesumistheproductisan−an−1an(−1)na0
Conjugate root theorem
AHL 2.12
For a polynomial with real coefficients, if a complex number z is a root, then the conjugate z⋆ must also be a root.
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