Find all real zeros of the polynomial f(x)= x^4 -130x^2+3969 and determine the mutiplicity of each.

Answer 1

let z = x^2

z^2 -130 z + 3969 = 0
(z- )(z- ) = 0
start factoring 3969
3969 = 3*3*3**3 *49 = 81*49
81+49 = 130 !!!!

(z-81)(z-49) = 0
so
x^2-49 = 0 ---> x = +7 or x = -7
x^2-81 = 0 ---> x = +9 or x = -9

Answer 2

Using the polynomial function f(x)=3x^4-5x^3+8x-6. According to the rational zero theorem, which of the following could not be a zero of the f(x)?