Problem 124 - College Algebra

Question

If you are given a quadratic equation, how do you determine which method to use to solve it?

Step-by-Step Solution

Answer

To find the method to solve a given quadratic equation, first, see if the equation is factorable. If not, see if completing the square is feasible. If neither of these methods seems suitable, solve the equation using the quadratic formula.

Step 1: Recognize the Form

Given a quadratic equation, first look at it and recognize its form. A quadratic equation has the standard form \( ax^2 + bx + c = 0 \) , where \( a, b, c \) are constants, and \( a \) is not equal to zero.

Step 2: Factoring

Check if the equation can be factored easily. If it can, then solving by factoring is the simplest method. If factors are not readily apparent, move to the next step.

Step 3: Completing the Square

Look at the quadratic equation to see if completing the square is feasible. If the coefficient of \( x \) or the constant term is a perfect square or can easily be adjusted to form a perfect square, then using this method is beneficial. If not, move to the next step.

Step 4: Quadratic Formula

If neither factoring nor completing the square seems feasible, apply the quadratic formula. The quadratic formula \( x = \[ -b ± sqrt(b^2 - 4ac) \] / 2a \) can solve any quadratic equation.