Question

This expression can be simplified to −8q^2−128q−312 and then written in factored form as −8(q−3)(q−13). What do the numbers 3 and 13 represent in the expression?

a. Solutions of the equation
b. Coefficients of the quadratic term
c. Constants in the linear terms
d. Exponents of the variable

Answer 1

The numbers 3 and 13 in the factored form −8(q−3)(q−13) are the solutions of the quadratic equation when it's set to zero.

Step-by-step explanation:

The numbers 3 and 13 in the factored form −8(q−3)(q−13) represent the solutions of the equation. When the equation is set equal to zero, these solutions are the values of 'q' that make the equation true (also known as the roots or zeros of the equation). To find the solutions using the quadratic formula, you would plug the corresponding coefficients into the formula. In this case, if you have a quadratic equation of the form at² + bt + c = 0, the numbers 3 and 13 would be derived from setting each factor equal to zero: q−3=0 and q−13=0, solving for 'q' in both cases.