Question

solve 2x2 − 3x + 6 = 0. x equals the quantity of 3 plus or minus i square root 39 all over 4 x equals the quantity of negative 3 plus or minus i square root 39 all over 4 x equals the quantity of negative 3 plus or minus square root 57 all over 4 x equals the quantity of 3 plus or minus square root 57 all over 4

Answer 1

We will use the quadratic formula to solve for the x values of this quadratic.
`x=(3+/-√(3^2-4(2)(6)))/(2(2))`. Simplifying that a bit gives us
`x=(3+/-√(9-48))/(4)` and
`x=(3+/-√(-39))/(4)`. We can't leave that negative under there. So we use the fact that -1 = i^2 and make the substitution.
`x=(3+/-√(i^2*39))/(4)`. i^2 is a perfect square that we can pull out, leaving us with
`x=(3+/-i√(39))/(4)`. The first of your choices above is the one that you want.