Pre Calculus

posted by .

1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^3+5x^2+3x


2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity 2 at x=1 and a zero at x=2+i

  • Pre Calculus -

    We see right off that x=0 is a root.

    Any rational roots must have a numerator which divides 3, and a denominator which divides 3. So, try 3,1,1/3

    Then we have x(x-1)(3x^2 - 8x + 3)
    The quadratic formula reveals the other two roots:

    4/3 +/- √7/3
    _____________________

    If 2+i is a root, so is 2-i, so x^2 -4x + 5 is a factor.

    So, f(x) = (x-1)(x-1)(x^2 - 4x + 5)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find all …
  2. Math

    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 …
  3. 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, …
  4. algebra

    Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (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 …
  5. algebra

    Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (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 …
  6. Algebra

    Consider the polynomial f(x) = 3x3 – 2x2 – 7x – 2. (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 …
  7. Math - potential zero

    List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely over the real numbers. Please show all of your work. f(x) = x^4 - 7x^3 -3x^2 + 19x + 14 Help
  8. Rational Zeros

    List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor f(x)=2x^4+19x^3+37x^2-55x-75
  9. calculus-can someone please help me with this ques

    Find all zeros of the following polynomial. Write the polynomial in factored form. f(x)=x^3-3x^2+16x-48 I put: x^2(x-3)+16(x=3) (x-3)(x^2+16) For zeros: x-3=0 x=0 **My teacher stated check the equation solution again. What is the value …
  10. Pre-Calculus

    Find all the rational zeros of the polynomial, and then find the irrational zeros P(x)= 2x^4+15x^3+31x^2+20x+4

More Similar Questions