solve the quadratic equation, 6x^2 - 3x + 6 = 0. Which of the following expresses its solutions in the form a ± bi?
1/2 ± √15/2 i
1/4 ± √17/4 i
-1/4 ± √15/4 i
1/4 ± √15/4 i
To solve the quadratic equation 6x^2 - 3x + 6 = 0, we can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation:
a = 6
b = -3
c = 6
Substituting these values into the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(6)(6))) / (2(6))
x = (3 ± √(9 - 144)) / 12
x = (3 ± √(-135)) / 12
x = (3 ± √(135)i) / 12
x = (1/4) ± (√15/4)i
Therefore, the solutions to the quadratic equation 6x^2 - 3x + 6 = 0 are given by:
x = 1/4 ± √15/4 i
Therefore, the answer is 1/4 ± √15/4 i.