SOLUTION: Identify the number of solutions of the equation or the number of zeros of the function. f(x) = {{{2x^4+x^2-7+x^6}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Identify the number of solutions of the equation or the number of zeros of the function. f(x) = {{{2x^4+x^2-7+x^6}}}      Log On


   

Question 825422: Identify the number of solutions of the equation or the number of zeros of the function.
f(x) = 2x%5E4%2Bx%5E2-7%2Bx%5E6
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since the domain of the function is an infinite set (all real numbers), then there are an infinite number of solutions to the function.

To find the number of zeros, we should first put the polynomial into standard form (with the exponents in highest to lowest order):
f%28x%29+=+x%5E6%2B2x%5E4%2Bx%5E2=7
This is a polynomial of degree 6. So within the set of complex numbers there will be 6 zeros.