Final answer:
To find the value of constant b where the solutions to the equation (t + 8/3)(t + b) = 0 are -(8/3) and (13/3), we identify that b must be equal to -(13/3).
Step-by-step explanation:
To find the value of b when -(8/3) and (13/3) are solutions to the equation (t + (8/3))(t + b) = 0, we first recognize that the structure of the equation indicates it has been factored into the product of two terms. According to the zero product property, if the product of two terms equals zero, then at least one of the terms must be zero. Therefore, we set each term equal to zero to find the solutions for t.
The given solutions of t are -(8/3) and (13/3). To find the constant b, we use the second term: if (13/3) is a solution, we have t + b = 0 when t = (13/3). Substituting this value of t into the equation gives us (13/3) + b = 0. Solving for b yields b = -(13/3).