Djamila is looking for conjugate pair solutions to the equation 3x^2 - 5x = -6. Which of the following options should she choose?
5/6 ± i√47/6
5/6 ± 5i/6
-5/6 ± i√47/6
5/6 ± 7i/6
To find the conjugate pair solutions to the equation, we need to find the roots of the equation. To start, we can rearrange the equation into the standard quadratic form:
3x^2 - 5x + 6 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = -5, and c = 6.
x = (-(-5) ± √((-5)^2 - 4(3)(6))) / (2(3)) = (5 ± √(25 - 72)) / 6 = (5 ± √(-47)) / 6
Since we have a square root of a negative number, we know that the solutions will be complex numbers and will have conjugate pairs.
Therefore, Djamila should choose the option 5/6 ± i√47/6 as the correct answer, as it represents the conjugate pair solutions to the equation.