Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive integers whose product is 110.

Key Concepts

Consecutive Integers

Consecutive integers are numbers that follow each other in order without any gaps. For example, if x is an integer, then the next consecutive integer is x + 1. In the context of the question, we are looking for two integers, which can be represented as x and x + 1, whose product equals 110.

Product of Integers

The product of two integers is the result of multiplying them together. In this case, we need to find two consecutive integers, x and x + 1, such that their product, expressed as x(x + 1), equals 110. This requires setting up the equation x(x + 1) = 110 and solving for x.

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants. In solving for the consecutive integers, we can rearrange the product equation into a standard quadratic form: x² + x - 110 = 0. This allows us to apply methods such as factoring or the quadratic formula to find the values of x.