Mathematics - Lecture 17 "Zeros of polynomials inverse functions". The main contents of the chapter consist of the following: Rational zero test, inverse functions, one-to-one functions, restriction of domain. | Zeros of Polynomials Inverse Functions Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 17 Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 1 / 61 Outline 1 Rational Zero Test 2 Inverse Functions 3 One-to-One Functions Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 2 / 61 Rational Zero Test Theorem Given a polynomial p(x) = an xn + an−1 xn−1 + · · · + a1 x + a0 with only integer coefficients and an = 0, if p , a fraction in lowest terms, is a zero of P (x), then p is a factor of a0 q and q is a factor of an . Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 3 / 61 Remarks: 1 The Rational Zero Test gives a finite set of “candidate” rational zeros. Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 4 / 61 Remarks: 1 The Rational Zero Test gives a finite set of “candidate” rational zeros. 2 The Rational Zero Test does not give all the zeros of the polynomial, as polynomials may have irrational zeros, Math 17 (UP-IMath) Polynomial Zeros, Inverse Functions Lec. 17 4 / .
