Question

I have been told that two roots of the equation x^4 - 5x^2+2x=0 are 0 and -2. It then asks me to find the two other roots. The method I have been given tells me to use the constant and check all the factors of the constant with the equation to find the roots. Since there is no constant, will you please help me find what to do?

Answer 1

if the roots are a and b then (x-a) and (x-b) are factors of the polynomial.
the highest exponent of the variable is 4 so there are 4 roots.

f(x) = (x-a)(x-b)(x-c)(x-d) roots a, b, c, d

f(x) divided by (x-a)(x-b) = (x-c)(x-d)

Answer 2

can you see f(x)/x(x+2) = a quadratic to be factored ?
when you factor that quadratic set = 0 solve to get the other roots