Solving Equations in Quadratic Form

Any equation in the form ax 2 + bx + c = 0 is said to be in quadratic form. This equation then can be solved by using the quadratic formula, by completing the square, or by factoring if it is factorable.

Example 1

Solve x 4 – 13 x 2 + 36 = 0 by (a) factoring and (b) applying the quadratic formula.

  1. equation%

    By the zero product rule, equation

  2. x 4 – 13 x 2 + 36 = 0

    is equivalent to equation

    When applying the quadratic formula to equations in quadratic form, you are solving for the variable name of the middle term. Thus, in this case, equation

    Using the square root property, equation

Example 2

Solve equation by (a) factoring and (b) applying the quadratic formula.

  1. equation

    In the last step on the right, equation must be a nonnegative value; therefore, equation has no solutions. The only solution is x = 36.

  2. equation is equivalent to equation equation

    When applying the quadratic formula to this quadratic form equation, you are solving for equation.

    equation

    There is no solution for equation. Thus, x = 36 is the only solution.