Djamila is looking for conjugate pair solutions to the equation 3x2−5x=−6 . Which of the following options should she choose?(1 point) Responses 56±7i6 Start Fraction 5 over 6 End Fraction plus or minus Start Fraction 7 i over 6 End Fraction −56±i47√6 negative Start Fraction 5 over 6 End Fraction plus or minus Start Fraction i Start Root 47 End Root over 6 End Fraction 56±5i6 Start Fraction 5 over 6 End Fraction plus or minus Start Fraction 5 i over 6 End Fraction 56±i47√6

Answer 1

To find the conjugate pair solutions to the equation 3x^2 - 5x = -6, we can rearrange the equation into the standard quadratic form:

3x^2 - 5x + 6 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -5, and c = 6.

Plugging in these values, we get:

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 are complex conjugates.

Therefore, Djamila should choose the option:

56±i√47/6