Final answer:
The negative solution to the quadratic equation 3x² - 2x = 16 is found using the quadratic formula, which yields two solutions: 8/3 and -2. The negative solution is -2, which corresponds to answer choice A) -2.
Step-by-step explanation:
The question asks for the negative solution to the quadratic equation 3x² - 2x = 16. To find the solution, we first want to set the equation equal to zero by subtracting 16 from both sides, yielding 3x² - 2x - 16 = 0.
To solve this quadratic equation, we can use the quadratic formula, which states that for any quadratic equation of the form ax² + bx + c = 0, the solutions for x can be found using x = (-b ± √(b² - 4ac))/(2a). Applying the quadratic formula to our equation, where a = 3, b = -2, and c = -16, we get:
x = (2 ± √((-2)² - 4(3)(-16)))/(2(3))
x = (2 ± √(4 + 192))/6
x = (2 ± √(196))/6
x = (2 ± 14)/6
Therefore, the solutions are x = (2 + 14)/6 = 16/6 = 8/3 and x = (2 - 14)/6 = -12/6 = -2, which is the negative solution we are looking for. Therefore, the correct answer is A) -2.