Question

f(x)=2x^4-18x^2
a. use Descartes Ruke of signs to determine the number of positive and negative roots.
B. Use the Rational Zero Theorem to determine a list of possible zero's
C. Use the Intermediate Value Theorem to prove that the polynomial has a zero in the interval [-6,-1].
D. solve for the zeros of f(x)

I came up with 0 possible negative root then got stuck

Answer 1

f(x)=2x^4-18x^2 becomes
f(x)=2x^2(x^2-9)
b) list of possible zeros, {0,0,3,-3}
c) f(-6)=2*36*36-18*36=144
f(-1)=2*1-18*1=-16
since the function is cts everywhere and one end of the interval is positive and the other negative then somewhere in between [-6,-1] exist a point for zero
d)2x^2(x^2-9)=0
means either 2=0 or x^2=0 or x^2-9=0 therefore x=0 and x=+3 and x=-3