We have degree 6, so it has 6 complex zeros. 3 complex zeros are given, therefore yje remaining 3 zeros are also complex. By the Conjugate Pairs Theorem they are: -i, 3 + 2i, -2 – i.

Question

asked 2021-02-11

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3, 2 and 2 - 3i are zeros, f(1) = -10

asked 2020-12-25

asked 2021-04-21

Polynomial calculations Find a polynomial f that satisfies the following properties. Determine the degree of f. then substitute a polynomial of that degree and solve for its coefficients.

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={9}{x}-{8}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={x}^{{{4}}}-{12}{x}^{{{2}}}+{30}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={9}{x}-{8}\)

\(\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={x}^{{{4}}}-{12}{x}^{{{2}}}+{30}\)

asked 2021-05-11

Consider the polynomial function \(p(x)=(3x^{2}-5x-2)(x-5)(x^{2}-4)\).

A) what is the degree of the polynomial? What is the y intercept of the function?

B)What are the zeros and their multiplicities?

C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?

A) what is the degree of the polynomial? What is the y intercept of the function?

B)What are the zeros and their multiplicities?

C) what is the leading term of the polynomial and what power function has a graph most similiar to the graph of p?

asked 2021-03-23

Five distinct numbers are randomly distributed to players numbered 1 through 5. Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially, players 1 and 2 compare their numbers; the winner then compares with player 3, and so on. Let X denoted the number of times player 1 is a winner. Find P{X = i}, i = 0,1,2,3,4.

asked 2021-05-01

Find all zeros of p(x), real or imaginary. \(p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27\) List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of \(p(x) = (x-c)(x^{3}+Ax^{2}+Bx+D)\) State the exact answer and a decimal approximation of each zero to the tenths place

asked 2021-04-06

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{23}{x}^{{{3}}}-{13}{x}^{{{2}}}+{32}{x}+{16}\)

\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{23}{x}^{{{3}}}-{13}{x}^{{{2}}}+{32}{x}+{16}\)

asked 2021-03-20

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{7}{x}^{{{3}}}-{12}{x}^{{{2}}}+{3}{x}+{2}\)

\(\displaystyle{P}{\left({x}\right)}={6}{x}^{{{4}}}-{7}{x}^{{{3}}}-{12}{x}^{{{2}}}+{3}{x}+{2}\)

asked 2021-05-20

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={3}{x}^{{{5}}}-{14}{x}^{{{4}}}-{14}{x}^{{{3}}}+{36}{x}^{{{2}}}+{43}{x}+{10}\)

\(\displaystyle{P}{\left({x}\right)}={3}{x}^{{{5}}}-{14}{x}^{{{4}}}-{14}{x}^{{{3}}}+{36}{x}^{{{2}}}+{43}{x}+{10}\)

asked 2021-04-02

Find all rational zeros of the polynomial, and write the polynomial in factored form.

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}-{3}{x}^{{{2}}}-{2}{x}+{3}\)

\(\displaystyle{P}{\left({x}\right)}={2}{x}^{{{3}}}-{3}{x}^{{{2}}}-{2}{x}+{3}\)