* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Document
Survey
Document related concepts
Field (mathematics) wikipedia , lookup
Gröbner basis wikipedia , lookup
History of algebra wikipedia , lookup
Horner's method wikipedia , lookup
Polynomial greatest common divisor wikipedia , lookup
Quadratic equation wikipedia , lookup
Factorization of polynomials over finite fields wikipedia , lookup
Cayley–Hamilton theorem wikipedia , lookup
Polynomial ring wikipedia , lookup
Cubic function wikipedia , lookup
Root of unity wikipedia , lookup
Quartic function wikipedia , lookup
Eisenstein's criterion wikipedia , lookup
System of polynomial equations wikipedia , lookup
Transcript
DAY #7 – JANUARY 16 TH , 2017 OBJECTIVE: TO USE THE FUNDAMENTAL THEOREM OF ALGEBRA TO SOLVE POLYNOMIAL EQUATIONS WITH COMPLEX SOLUTIONS Warm-up Use the rational root theorem to solve the following polynomial function. 𝑦 = 6𝑥 3 − 14𝑥 2 + 8 Conjugate Root Theorem If p(x) is a polynomial with rational coefficients, then irrational roots of p(x) = 0 that have the form a + 𝑏 occur in conjugate pairs. That is if a + 𝑏 is an irrational root with a and b rational, then a − 𝑏 is also a root. If p(x) is a polynomial with real coefficients, then the complex roots of p(x) = 0 occur in conjugate pairs. That is, if a + bi is a complex root with a and b real, then a – bi is also a root. Example: A quartic polynomial p(x) has rational coefficients. If 2 and 1 + 𝑖 are roots of p(x) = 0, what are the two other roots? Finding Roots using a graphing calculator.