Question

Using the quadratic formula to solve 2x2 = 4x – 7, what are the values of x?
2 plus-or-minus StartRoot 10 EndRoot i
1 plus-or-minus StartRoot 10 EndRoot i
StartFraction 2 plus-or-minus StartRoot 10 EndRoot i Over 2 EndFraction
1 plus-or-minus StartRoot 5 EndRoot i

Answer 1

2x^2 = 4x − 7 => 2x^2 − 4x + 7 = 0. With a=2, b=−4, c=7,

x = [−b ± √(b^2 − 4ac)]/(2a) = [4 ± √(16 − 56)]/4 = [4 ± √(−40)]/4
= [4 ± 2i√10]/4 = (2 ± i√10)/2 = 1 ± (i√10)/2.

So the correct choice is: (2 ± √10 i)/2.