When solving quadratic equations, it is important to remember that:

• Any positive number has two square roots, one positive and one negative, because there are two numbers that can be squared to make that number. (For example, and both equal 36, so 6 and -6 are both square roots of 36.)
• The square root symbol () can be used to express the positive square root of a number. For example, the square root of 36 is 6, but it can also be written as because .
• To express the negative square root of a number, say 36, we can write -6 or .
• When a number is not a perfect square—for example, 40—we can express its square roots by writing and .

How could we write the solutions to an equation like ? This equation is saying, “something squared is 11.” To make the equation true, that something must be or . We can write:

A more compact way to write the two solutions to the equation is .

About how large or small are those numbers? Are they positive or negative? We can use a calculator to compute the approximate values of both expressions:

We can also approximate the solutions by graphing. The equation is equivalent to , so we can graph the function and find its zeros by locating the -intercepts of the graph.

Function on a grid. X axis from negative 14 to 2, by 2’s. Y axis from negative 14 to 2, by 2’s. Origin, O. Parabola opens upward and crosses the x axis at negative 7 point 3 1 7 and negative 0 point 6 8 3.