Now that the polynomial is in factored form, we can quickly see how many solutions there are to the original equation x⁴-3x³+6x²-12x+8=0.

4 solutions

Step-by-step explanation:

Given that

x⁴-3x³+6x²-12x+8=0.

The above equation is 4 th order equation because the highest power of x is 4.

As we know that n th order of equation have n number of solution and these solution is known as roots of the equation.

So the above equation have 4 solutions.

The solution of given equation is

x = - 0.47 + 1.42 i

x = - 0.47 - 1.42 i

x = 0.85 + 0.39 i

x = 0.85 - 0.39 i