What are the following roots of the polynomial x3-6x2 plus 7x-2?

Answer 1

x3 - 6x2 + 7x - 2 = x3 - x2 - 5x2 + 5x + 2x - 2

= x2(x - 1) - 5x(x - 1) + 2(x - 1)

= (x - 1)(x2 - 5x + 2)

= (x - 1){x - 0.5*[5 - sqrt(25 - 8)]}){x + 0.5*[5 - sqrt(25 - 8)]}

= (x - 1)(x - 0.4384)(x - 4.5616)

so that the roots are

x = 1

x = 0.4384

and

x = 4.5616