how do I find the zeros for this equation: x^5-2x^3+1?

Question

I'm stuck, I'm in calculus but can't remember how to factor this one out to find the zeros.

Answer 1

x=1 and x=-1 are NOT solutions
take y =x^5 -2x^3 +1
y´= 5x^4-6x^2 = x^2(5x^2-6)=0 x=0 and x= +-sqrt(6/5)
sign of y´ ++++ -sqrt(6/5) ------------- sqrt(6/5)+++++++
y(-sqrt6/5)>0 y(sqrt6/5) <0

y decreases from -sqrt(6/5) local max to sqrt(6/5) local min
There are three roots
one less than -sqrt(6/5) one less but near to sqrt6/5 and the third greater but also near to sqrt6/5

Answer 2

i think the zeroes will probably be either +1 or -1 since the constant +1 has the above two factors
sustitute +1 and -1 for all x in the polynomial the one is the zero which gives the answer as 0 after substituting



hope u got it.......