solving a quadratic equation 2x²-4x+3=0

Question

2x²-4x+3=0.

Answer 1

Given equation 2 x ^2 - 4 x + 3 =0.

Compare to the quadratic form a x ^2 + b x + c = 0.

a = 2, b = - 4, c = 3.

x = [- b ± √(b ^2 - 4ac]/2a

x = [ 4 ± √(16 - 4*2*3)]/4

x = [4 ± √(16 - 24)]/4

x = [4 ± √-8 ]/4

i^2 = - 1.

x =[ 4 ± √8i^2]/ 4

x =[4 ± 2√2i^2]/ 4

x =[2 ± √2i] / 2

x = [ 1 ± i /√2 ]

x =1 + i / √2 and  x =1 - i / √2

Solution : x = 1 + i /√2 and  x = 1 - i /√2.