Factoring Polynomials 2x^2-2x+3

Question

please  help!

Answer 1

Given polynomial 2x^2-2x+3

Compare it quadratic equation ax^2+bx+c = 0

a = 2, b = -2, c = 3

Roots are x = [-b+sqrt(b^2-4ac)]/2a and x = [-b-sqrt(b^2-4ac)]/2a

x = [2+sqrt(4-4*2*3)]/2*2   and  x = [2-sqrt(4-4*2*3)/2*2]

x = (2+sqrt(-20))/4 and x = 2-sqrt(-20))/4

x = (2+2sqrt(-5))/4 and x = 2-2sqrt(-5))/4

x = 2(1+sqrt(-5))/4  and x = 2(1-sqrt(-5))/4

Given polynomial has imagnary roots.

x = (1+2.23i)/2   and  x = (1-2.23i)/2

Factoring of 2x^2-2x+3 =[x-(1+2.23i)/2][x-(1-2.23i)/2]