Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and 2-2i.
- Review Andrews work, identify the error and correct all the work from that point forward that is affected by this error.
- Include at least one sentence explaining his error. use mathematical vocabulary
Hello, thank you for reading :) Would you please help me on this
(x -3) ( [ x - (2+2i) ] [ x - (2 - 2i)] = 0
(x - 3) [ x^2 - (2 - 2i)x - (2 + 2i)x + (2 + 2i) ( 2 -2i) ] = 0
(x - 3) [ x^2 - 4x + 4 - 4i^2 ] = 0 [ i^2 = -1 ]
(x - 3) [ x^2 - 4x + 8] = 0 The error occurs in the second step [ -4x instead of 4x ]
x^3 - 4x^2 + 8x - 3x^3 + 12x - 24 = 0
x^3 - 7x^2 + 20x - 24 = 0