Find a polynomial with real coefficients that has the given zeros.- 1 and 4-5iOne such polynomial P(x) can be defined as P(x) =x - 7x+x+41.– 7x?%3DHelp me solve thisView an exampleTextbook

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Answered: Find a polynomial with real…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 10CT

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Practice: Determine how many zeros each polynomial function has. Two zeros of P(x)=3x2(x714x+3) are 0 How many other zeros are there?
Write a third-degree polynomial function with real coefficients and the given zeros. 4,i
Self Check Find a second degree polynomial function P(x) with real coefficients that has a zero of 1i
(a) If a is a zero of polynomial P. then _________mustbe a factor of P(x). (b) If a is a zero of multiplicity m of the polynomial P, then _______must a factor Of P(x) when we factor P completely.
Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _______of the polynomial. Then we find the intervals determined by the real____ and use test points in each interval to find the sign of the polynomial on that interval. Let P(x)=x(x+2)(x1) Fill in the diagram below to find the intervals on which P(x)0. From the diagram above we see that P(x)0 on the intervals _____ and _____ .
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?

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Find a polynomial with real coefficients that has the given zeros. -1 and 4-5i One such polynomial P(x) can be defined as P(x) =x - 7x+x+41.