please help!

Question

Factoring Polynomials 2x^2-2x+3

Answer 1

Given polynomial is 2x^2-2x+3

Compare it quadratic form is ax^2+bx+c

Roots are x = [-b±√(b^2-4ac)]/2a

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

Roots are x = [2±√(4-4*2*3)]/2*2

x = [2±√(4-24)/4

x = [2±√-20]/4

Here the given polynomial has imaginary roots.

x = [2±√(4*-5)]/4

x = [2±2√-5]/4

x = 2[1±√5i]/4

x = (1±√5i)/2

x = (1+√5i)/2 and x = (1-√5i)/2

Factoring of given polynomal is [2x-(1+√5i)][2x+(1+√5i)]