Final answer:
The value of constant k is found by setting the sum of the solutions of a quadratic equation, -b/a, equal to k(4a + b) and solving for k.
Step-by-step explanation:
The sum of the solutions of a quadratic equation, represented by the form at² + bt + c = 0. According to the standard properties of quadratic equations, the sum of the solutions (roots) can be found using the formula -b/a. In the question, it's given that the sum of the solutions is equal to k(4a + b), which suggests that -b/a should be equivalent to k(4a + b). Solving for k requires equating these two expressions and simplifying.
Setting -b/a equal to k(4a + b) gives: -b/a = k(4a + b). To find the value of k, you can divide both sides of the equation by (4a + b) and then multiply by -a, which leads to k = -b/a(4a + b). Therefore, the value of k depends on the values of a and b provided in the quadratic equation.