How to find the polynomial function with real coefficients, degree 5, zeros 1+i, -3, and 5,...

How to find the polynomial function with real coefficients, degree 5, zeros 1+i, -3, and 5, and P(0)=30 and P(4)= -70?

Expert Solution

milcah answered 2 years ago

1] Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are...

1] Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 2 and 5i are zeros; f(1) = 52 f(x)= ? (Type an expression using x as the variable. Simplify your answer.) 2] Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it...

If f is a polynomial of degree 3 or more how would you use real zeros...

If f is a polynomial of degree 3 or more how would you use real zeros of f to determine the open intervals over which f(x) > 0 or f(x) < 0. How and where does the sign of f change.

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using...

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n= 4; -1,4, and 4+2i are zeros f(1)=-156

Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient...

Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient of 1, and with the given zeros. 1+3i, -1, and 2?

use the Rational Zeros Theorem to find all the real zeros of each polynomial function given...

use the Rational Zeros Theorem to find all the real zeros of each polynomial function given below: f(X)=3X^3 + 6X^2 -15X - 30 f(X) = 2X^4 - X^3 - 5X^2 + 2X + 2

1. List the possible rational zeros of the the polynomial function. Do not find the zeros....

1. List the possible rational zeros of the the polynomial function. Do not find the zeros. f ( x ) = 3 x 5 − 5 x 2 + 6 x − 1 A) ± 1 , ± 3 B) ± 1 , ± 1 3 C) ± 1 , ± 1 3 , ± 3 D) ± 3 , ± 1 3 Group of answer choices A B C D 2. Find zeros and write the polynomial in factored...

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given...

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −5, 1, 2; f(3) = 48 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −3, −2, 0; f(−4) = 24 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −2i, 2i, 5; f(1) = 40 Find the zeros of f(x), and state the multiplicity of each zero. (Order your...

8. All the real zeros of the given polynomial are integers. Find the zeros. (Enter your...

8. All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x) = x3 + 6x2 − 32 x = Write the polynomial in factored form. P(x) = 9. Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x) = 4x4 − 45x2 + 81 x = Write the polynomial in factored form. P(x) =...

Below is the graph of a polynomial function f with real coefficients.

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of fare shown in the graph. (a) The function f is increasing over which intervals? Choose all that apply. (-∞ , -8) (-8, -5) (-8, -2) (-2, 3) (7, 9) (9, ∞) (b) The function f has local maxima at which x-values? If there is more than one value separate them with commas. (c) What...

Prove that every polynomial having real coefficients and odd degree has a real root

Problem: Prove that every polynomial having real coefficients and odd degree has a real root This is a problem from a chapter 5.4 'applications of connectedness' in a book 'Principles of Topology(by Croom)' So you should prove by using the connectedness concept in Topology, maybe.

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