Problem 172 - College Algebra

Question

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The quadratic formula is developed by applying factoring and the zero-product principle to the quadratic equation \(a x^{2}+b x+c=0\)

Step-by-Step Solution

Answer

The statement is false. The correct statement: The quadratic formula is developed by applying the method of completing the square to the quadratic equation \(a x^{2}+b x+c=0\)

Step 1: Analyze the original statement

In the original statement, it is claimed that the quadratic formula is derived by applying factoring and the zero-product principle. This is false. The method of completing the square is used to derive the quadratic formula.

Step 2: Correct the statement

Having established the error in the original statement, the correct statement would be: The quadratic formula is developed by applying the method of completing the square to the quadratic equation \(a x^{2}+b x+c=0\).