algebra

posted by .

Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots

  • algebra -

    work backwards from 4 imaginary roots (remember they come in complex conjugate pairs)
    (x-i)(x+i)(x-2i)(x+2i) = 0
    (x^2+1)(x^2+4)= 0
    x^4 + 5 x^2 + 4 = 0

  • algebra -

    Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 2

    I am trying to factor a 4th degree polynomial that does not have any rational roots. I need to somehow get it factored into two quadratics. Anyone know of a method to use. 3x^4 - 8x^3 - 5x^2 + 16x - 5 Two of the irrational roots are …
  2. 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 …
  3. Math - Fundamental Theorem

    We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate pairs). …
  4. Algebra 2

    How do I solve polynomial equation by finding all complex roots?
  5. Math

    State the number of complex roots,possible number of real roots and possible rational roots for x^5 - x^3 - 11x^2+ 9x+18=0
  6. Math (Algebra)

    For each degree 17 polynomial f with real coefficients, let sf be the number of real roots (counted with multiplicity). Let S be the set of all possible values of sf. What is |S|?
  7. algebra

    if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have?
  8. Algebra

    7. Describe the number and type of roots for the polynomial (how many real and complex?
  9. Math

    Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots <--?
  10. Precalculus

    There is at least one polynomial with real functions with 9+i as its only nonreal zero. A. The statement is​ false, because the Fundamental Theorem of Algebra dictates that there must be n complex zeros for a polynomial of degree …

More Similar Questions