Question

What are the roots of the polynomial equation 3x^4+12x^2=6x^3

Answer 1

Factor the equation to give
$3x^4+12x^2=6x^3$
$3x^4+12x^2-6x^3=0$
$x^2(3x^2+12-6x)=0$
By the zero product property, either x^2=0 or (3x^2+12-6x)=0 or both.
If x^2=0, then x=0
if (3x^2+12-6x)=0, we use the quadratic formula to solve for x
where x=1 ± √ (3) i

Answer: the roots of 3x^4+12x^2=6x^3 are {0 (multiplicity 2), 1+√3 i, 1-√3 i}