Math

Suppose $p(x)$ is a monic cubic polynomial with real coefficients such that $p(3-2i)=0$ and $p(0)=-52$.

Determine $p(x)$ (in expanded form).

  1. 👍 0
  2. 👎 0
  3. 👁 456
asked by Eka
  1. john is 30 pounds heavier than peter. their total weight 235 pounds.find johns weight

    1. 👍 0
    2. 👎 0
    posted by sam
  2. peter is 30 lbs lighter than john. So,

    j + j-30 = 235

    Odd; I expected an integer answer...

    as for the polynomial, who knows? I see no question there. And LaTex doesn't do well here. And p(x) cannot be monic with real coefficients and have a complex root.

    1. 👍 0
    2. 👎 0
    posted by Steve
  3. ah, actually I misspoke.

    Since 3+2i is also a root, we have

    p(x) = (x-(3-2i))(x-(3+2i))(x-a)
    = (x^2-6x+13)(x-a)

    So, now just solve for a:

    p(0) = -13a = -52
    a = 4

    p(x) = (x^2-6x+13)(x-4) = x^3-10x^2+37x-52

    1. 👍 0
    2. 👎 0
    posted by Steve
  4. Thanks so much :)

    1. 👍 0
    2. 👎 0
    posted by Eka

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    For every positive integer n, consider all monic polynomials f(x) with integer coefficients, such that for some real number a x(f(x+a)−f(x))=nf(x) Find the largest possible number of such polynomials f(x) for a fixed n

    asked by GT on July 10, 2013
  2. Algebra

    f(x)is a monic cubic polynomial with real coefficients. f(x) has 7+4i as a root and f(0)=−2145 . What is the coefficient of x in f(x) ?

    asked by Tony on May 23, 2013
  3. algebra!!!! please help me!!!!

    A number is called algebraic if there is a polynomial with rational coefficients for which the number is a root. For example, √2 is algebraic because it is a root of the polynomial x^2−2. The number √(2+√3+√5)is also

    asked by bob on May 22, 2013
  4. functions

    Suppose p (x) is a polynomial with real coefficients and p (4 + 9i)=0. What is p(4-9i)?

    asked by jerson on November 17, 2008
  5. heeeelp math

    Find the number of polynomials f(x) that satisfy all of the following conditions: f(x) is a monic polynomial, f(x) has degree 1000, f(x) has integer coefficients, f(x) divides f(2x^3+x)

    asked by lin on July 9, 2013
  6. heeelp math2

    Find the number of polynomials f(x) that satisfy all of the following conditions: f(x) is a monic polynomial, f(x) has degree 1000, f(x) has integer coefficients, f(x) divides f(2x^3+x)

    asked by lin on July 10, 2013
  7. Algebra

    I don't even know where to start, teacher gave us this with no direction. Suppose the polynomial R(x)=a9x^9+a8x^8+...+a,x+a0 has real coefficients with a9 cannot equal 0. Suppose also that R(x)has the following zeros: 5, 6, 5+5i.

    asked by Rachal on February 4, 2011
  8. maths

    Suppose p(x)=ax^2+bx+c is a quadratic polynomial with real coefficients and |p(x)|≤1 for 0≤x≤1. Find the largest possible value of |a|+|b|+|c|.

    asked by maths on July 9, 2013
  9. Math

    What are the coefficients in the polynomial 4x^2+3x-3? I'm not posting this to get the exact answer, I just need help on finding the coefficients. I'm not real good with polynomials, and I've been struggling a little. I just need

    asked by Jordan on May 9, 2018
  10. calculus--please help!!

    I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x)

    asked by Paul on December 27, 2012

More Similar Questions