Given x^4 − 4x^3 = 6x^2 − 12x, what are the approximate values of the non-integral roots of the polynomial equation?

the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27.

Step-by-step explanation:

To find the roots of the polynomial equation, we need to factorize the equation:

x^4 − 4x^3 = 6x^2 − 12x ⇒ x^4 − 4x^3 -6x^2 +12x = 0

⇒ x(x+2)(x -3 + sqrt(3))(x -3 - sqrt(3))

Then, the non integral roots are:

x1 = 3 - sqrt(3) = 1.26 ≈ 1.27

x2 = 3 + sqrt(3) =  4.73

Then, the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27