Example Question #1 : Identification
has two distinct solutions. What is their sum?
It is not necessary to actually find the solutions to a quadratic equation to determine the sum of its solutions.
First, get the equation in standard form by subtracting from both sides:
If a quadratic equation has two distinct solutions, which we are given here, their sum is the linear coefficient . In this problem, , making the correct choice.
Example Question #2 : Identification
The graph of the polynomial function
has one and only one zero on the interval . On which subinterval is it located?
The Intermediate Value Theorem (IVT) states that if the graph of a function is continuous on an interval , and and differ in sign, then has a zero on . Consequently, the way to answer this question is to determine the signs of on the endpoints of the subintervals - . We can do this by substituting each value for as follows:
assumes positive values for and negative values for . By the IVT, has a zero on .