Question

Factor the trinomial 15y^2-6y+2

Answer 1

Given trinomial is 15y^2-6y+2

Compare it quadratic form ax^2+bx+c

a = 15, b = -6, c = 2

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

x = 6+sqrt(36-4*15*2)/2*15            and      x = [6-sqrt(36-4*15*2]/2*15

x = 6+sqrt(36-120)/30                    and      x = [6-sqrt(36-120)]/30

x = 6+sqrt(-84)/30                         and      x = [6-sqrt(-84)/30

x = [6+2sqrt(-21)/30                      and      x = [6-2sqrt(-21)]/30

Given polynomial has imaginary roots.

x = 2[3+4.58i]/30                          and     x = 2[3-4.58i]/30

x = (3+4.58i)/15                           and     x = (3-4.58i)/15

Factoring of 15y^2-6y+2 is [x-(3+4.58i)/15][x-(3-4.58i)/15]