Home | | Maths 12th Std | Summary

# Summary

Vieta’s Formula for polynomial equations of degree 2,3, and n>3.

SUMMARY

In this chapter we studied

·               Vieta’s Formula for polynomial equations of degree 2,3, and n>3.

·               The Fundamental Theorem of Algebra : A polynomial of degree ≥ 1 has at least one root in C.

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

pairs, if the coefficients of the polynomial are real.

·               Rational Root Theorem : Let an xn+…+a1 x+ a0 with an ≠  0 and a0≠ 0 , be a polynomial with integer coefficients. If p/q , with ( p, q) = 1, is a root of the polynomial, then p is a factor of a0 and q is a factor of an.

·               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.

·               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
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
12th Mathematics : UNIT 3 : Theory of Equations : Summary | Theory of Equations