Vietaâ€™s Formula for polynomial equations of degree 2,3, and n>3.

**SUMMARY**

In this chapter we studied

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Vietaâ€™s Formula for polynomial equations of degree 2,3, and *n*>3.

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**The Fundamental Theorem of Algebra **: A polynomial of
degree *n *â‰¥ 1 has at least one root in **C**.

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**Complex Conjugate Root Theorem **: Imaginary (nonreal
complex) roots occur as conjugate

pairs, if the coefficients of the polynomial are real.

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**Rational Root Theorem **: Let *a*_{n}* x*^{n}*+â€¦+a*_{1} *x+* *a*0 with *a** _{n}* â‰ 0 and

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Methods to solve some special types of polynomial equations like
polynomials having only even powers, partly factored polynomials, polynomials
with sum of the coefficients is zero, reciprocal equations.

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**Descartes Rule : **If *p *is the number of positive roots of
a polynomial *P*(*x*) and *s *is the number of sign changes
in coefficients of *P*(*x*) , then *s *- *p *is a
nonnegative even integer.

Tags : Theory of Equations , 12th Mathematics : UNIT 3 : Theory of Equations

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12th Mathematics : UNIT 3 : Theory of Equations : Summary | Theory of Equations

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