### All HiSET: Math Resources

## Example Questions

### Example Question #1 : Zeroes Of Polynomials

The equation

has two distinct solutions. What is their sum?

**Possible Answers:**

**Correct answer:**

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 #41 : Algebraic Concepts

The graph of the polynomial function

has one and only one zero on the interval . On which subinterval is it located?

**Possible Answers:**

**Correct answer:**

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 .

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