Final answer:
To find the sum of the solutions of the quadratic equation 2x² - 3x - 2 = 0, we use Viète's formulas which dictate that the sum is equal to −b/a. In this equation, the sum is 1.5, and if rounded to the nearest whole dollar, Andy's brother would receive B. $2.
Step-by-step explanation:
The question involves solving a quadratic equation and finding the sum of its solutions.
The equation given is 2x² - 3x - 2 = 0.
To find the solutions for this equation, we use the quadratic formula, which is x = −b ± √(b² - 4ac) / (2a), where a, b, and c are the coefficients of the equation.
Plugging the values from the equation into this formula:
a = 2, b = -3, and c = -2.
The quadratic formula gives us the two solutions for x.
However, according to Viète's formulas, the sum of the solutions of a quadratic equation is equal to −b/a.
In this case, the sum is −(−3)/2, which simplifies to 3/2 or 1.5.
Since the sum of solutions is 1.5, Andy will give his brother $1.50, which is not among the options provided.
If the answers are supposed to be whole dollars, we could assume the question intends for us to round to the nearest whole number, which would be \$2. Hence, the closest option and likely intended answer is B. $2.