#  >> K-12 >> AP Classes

How to Determine How Many Solutions Are in Quadratic Equations

Quadratic equations model a parabolic path in two-dimensional space. The commonly performed operation when dealing with quadratic equations is to solve for the roots, also known as the zeros of the polynomial, to determine the "solutions" to the equation. The solutions are the points where the parabolic curve crosses the x-axis. The solution points are useful because they can subsequently be used to determine all other points on the parabola. However, in some situations one of these points is illegitimate and must be disregarded.

Instructions

    • 1

      Factor the quadratic equation using the quadratic formula. This yields two binomial factors. If a negative number occurs within the square root then both solutions are deemed illegitimate and disregarded. This is the first point where solutions may be disregarded.

    • 2

      Solved each binomial factor for its value of "x." For example, x^2 - 2x - 8 factors to (x + 2) and (x - 4). Solving these factors for "x" yields x = -2 and x = 4, respectively.

    • 3

      Examine the situation that the quadratic equation models. For example, a common physics problem involves examining the parabolic flight of an object that has been thrown off a building. Solving the quadratic equation that models this flight yields two answers. However, the smallest answer, often a negative number, will be a point measuring parabolic flight before the object actually began moving. Because the object was thrown from the building it doesn't begin a parabolic trajectory until after that first solution point. Therefore, the first solution point in that quadratic equation is disregarded.

Learnify Hub © www.0685.com All Rights Reserved