Final answer:
To determine the correct constant term in a quadratic equation when given the roots, we use the product of the correct roots (6 and 4) to find the constant term. Since 6 * 4 = 24, the correct constant term in the equation is 24. This showcases the importance of correct arithmetic operations in solving equations.
Step-by-step explanation:
The student's question involves finding the correct constant term in a quadratic equation when given the solutions to the equation. We know that if the roots of a quadratic equation ax2 + bx + c = 0 are m and n, then the sum of the roots is -b/a and the product of the roots is c/a. Given that Rocky found the roots to be 8 and 2, the product of his roots would have been 16. However, the correct roots are 6 and 4, so the correct product of the roots is 24.
Rocky's incorrect solution suggests that his mistaken constant term, which is the product of the roots times the leading coefficient (assuming the leading coefficient a = 1), was 16. To find the correct constant term, we multiply the correct roots 6 and 4 to get 24. Therefore, the correct constant term in the equation is 24.
Additionally, we must remember that the roots of a quadratic equation are based on correct arithmetic operations, regardless of the context or the era. Incorrect operations lead to incorrect results, as demonstrated in the mistake Rocky made. Understanding how to solve for variables is essential in mathematics, and it is important to always verify the accuracy of each step in solving equations.