The equation f(x) = 2x⁶ - 4x⁴ + 15x² + 100 has 6 zeros.
To find the zeros of the given polynomial equation
f(x) = 2x⁶ - 4x⁴ + 15x² + 100 , we need to set the equation equal to zero and solve for x:
2x⁶ - 4x⁴ + 15x² + 100=0
The number of solutions to this equation, or the number of zeros, corresponds to the degree of the polynomial. In this case, the degree is 6, so there are six complex solutions, counting multiplicity.
Solving a sextic (degree-six) equation analytically can be challenging, and often, numerical methods or advanced techniques are employed. The solutions may involve a combination of real and complex roots, and some roots may be repeated.