How do you solve a^3-2a^2+4a=0

Answer 1

divide by a

factor out an a

a(a^2 -2a + 4) =0

set each factor =0 and solve for a

a=0 is one solution and the only real solution

but 3 degree equations have 3 solutions. 2 are imaginary for this equation

a^2-2a +4 =0

a = 2/2 + or - (1/2)sqr(4-16) = 1 + or - isqr3

a = 1+isqr3 or 1-isqr3

or you could solve by completing the square

a^2 -2a +1 =-4 +1 =-3

a-1 = + or - sqr(-3)

a = 1 + or -isqr3