Question

supply the number so that the quadratic equation below has 6 and 8 as its solutions.

x^2 - 14x + ___ = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the missing number in the quadratic equation, we can use the fact that the sum of the solutions of a quadratic equation is equal to the opposite of the coefficient of the linear term divided by the coefficient of the quadratic term.

In this case, the coefficient of the linear term is -14 and the coefficient of the quadratic term is 1. Therefore, the sum of the solutions is 14/1 = 14.

Given that the solutions are 6 and 8, their sum is 6 + 8 = 14. So, the missing number is the product of the solutions, which is 6 * 8 = 48.

Therefore, the quadratic equation is:
x^2 - 14x + 48 = 0