According to the fundamental theorem of algebra, how many zeros does the function f(x) = 17x15 + 41x12 + 13x3 − 10 have?

2 Answer

  • It should have 15 solutions.
    The number of solutions depends on the term with with the highest exponent.

  • Answer: The given expression should  have 15 zeroes


    Fundamental theorem of algebra says the polynomial that have complex coefficient  and highest power that is degree must have one complex root this involves real number because every real number  is an imaginary number where imaginary part is equal to zero

    General representation of complex number a+ib ; a and b are real numbers.

    Number of zeroes depends on the degree of polynomial

    Number of zeroes is equal to the highest power which is degree

    Here degree is 15  hence, number of zeroes will be 15.