Ask questions and get helpful answers.

Find the polynomial function f with real coefficients that has given degree, zeros, and solution point.

Degree: 3
Zeros: -2,1- root of 2i
Solution point: f(-1)=-54

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
1 answer
  1. since complex solutions appear in conjugate pairs, the third solution must be 1 + √2 i
    so the function has the form
    f(x) = a(x+2)(x - 1 + √2 i)(x - 1 - √2 i)
    = a(x-2)(x^2 - 2x + 3)
    since f(-1) = a(-3)(1 + 2 + 3) = -18a
    so -18a = -54
    a = 3

    f(x) = 3(x+2)(x^2 - 2x + 3)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Similar Questions

  1. Algebra

    Write a polynomial of least degree with real coefficients and with the root -6-8i. Write your answer using the variable x and in standard form with a leading coefficient of 1. Thanks, I have no idea!

  2. algebra

    Please help!!! Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some

  3. Math Help Please

    Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 3, and 1 –2i as zeros. Find the remaining zero. A. –2 B. –1 – 2i C. 0 D. 1 + 2i

  4. algebra

    Find a polynomial function P(x) with the given zeros. There is no unique answer for P(x). −2, 8 P(x) =

  5. Math

    Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k. Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k Q.3)If 2 and 3 are the zeroes of the polynomial 3x2-2kx+2m find the values of k

  6. Algebra

    Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have

  7. College Algebra

    Find a polynomial function f(x), with real coefficients, that has 1 and 3+2i as zeros, and such that f(-1)=2 (Multiply out and simplify your answer)

  8. Math

    Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial function of odd degree may have

  9. Algebra 2

    Explain why a polynomial function with an odd degree must have at least one real zero

  10. pre-calculus math

    A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i; degree 3

Still need help?

You can ask a new question or browse existing questions.