Find a polynomial with integer coefficients that satisfies the given conditions.R has degree 4 and zeros 3 - 4i and 4, with 4 a zero of multiplicity 2.R(x) =

Given: R has degree 4 and zeros 3 - 4i and 4, with 4 a zero of multiplicity 2.

Answered: Find a polynomial with integer…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 9T

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Similar questions

The polynomial P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________
If the polynomial function P(x)=anxn+an1xn1+....+a1x+ao< has integer coefficients. then the only numbers that could possibly be rational zeros of P are all of the form pq, where p is a factor of _________and q is a factor of _______________. The possible rational zeros of P(x)=6x3+5x219x10 are __________________________.
a. Find a nonconstant polynomial in Z4[ x ], if one exists, that is a unit. b. Find a nonconstant polynomial in Z3[ x ], if one exists, that is a unit. c. Prove or disprove that there exist nonconstant polynomials in Zp[ x ] that are units if p is prime.
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
True or False? If a is an upper bound for real zeros of the polynomial P, -a is necessarily a lower bound for the real zeros of P.

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Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 3 - 4i and 4, with 4 a zero of multiplicity 2. R(x) =