Question

Find the roots of the given problem:

x^5-8x^4+28x^2-56x^2+64x-32

Answer 1

I know that one of the roots is 2. The roots also cannot be -1,1,-2,4,-4,8

Answer 2

The only possible options left are +16,-16,-8,32,-32

Answer 3

Okay, so you use synthetic division with the two and keep going, then you use the -b plus or minus the square root of b^2-4(a)(c)/2a ?

Answer 4

I believe that 28x^2 have been written, 28x^3. ?

Answer 5

You are right

Answer 6

From Mathematica, the factors are:\[(x-2)^3 \left(x^2-2 x+4\right) \]

Answer 7

The values for x that make the expression zero are:\[\left\{\{x\to 2\},\{x\to 2\},\{x\to 2\},\left\{x\to 1-i \sqrt{3}\right\},\left\{x\to 1+i \sqrt{3}\right\}\right\} \]