Find all the real zeros of the polynominal function Determin

Find all the real zeros of the polynominal function. Determine the multiplicity of each zero and the number of turning points of the graphy of the function. Use a graphing utility to graph the function and verify your answers.

f(x) = x⁵ + x³ - 6x

Solution

f(x)=x⁵+x^3 -6x = x(x^4 +x^2-6) =x(x^2 +3)(x^2-2)

for zeroes we have t set f(x)=0

x(x^2+3)(x^2-2)=0

x=0 multiplicity 1

x=-sqrt2 multiplicity 1

x=sqrt 2 multiplicity 1

mulber of turning points=3