Find all real and complex roots for the following polynomlal

Find all real and complex roots for the following polynomlals. IlI. Theorem to identify potential roots. the Ration Ul 17, g(x)=xt-1

x^3 - 1 = 0

we can see that x = 1 is the first root of equation

x1 = 1

the (x^3 - 1)/(x - 1) = x^2 + x + 1

Now the roots of

x^2 + x + 1 = 0

will be

x = [-1 +/- sqrt (1^2 - 4*1*1)]/2

x2 = [-1 + sqrt 3]/2

x3 = [-1 - sqrt 3]/2

17.

x^4 - 1 = 0

(x^2)^2 - 1^2 = 0

Now we know that

a^2 - b^2 = 0,

then

(a - b)(a + b) = 0

So,

(x^2 - 1)(x^2 + 1) = 0

x^2 - 1 = 0

x = +1 or x = -1

x^2 + 1 = 0

x^2 = -1

x = (-1)^0.5

then x = +i Or x = -i