Problem 171
Question
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Any quadratic equation that can be solved by completing the square can be solved by the quadratic formula.
Step-by-Step Solution
Verified Answer
The statement is True.
1Step 1: Understand the Concepts
Understand what is meant by the terms quadratic equation, completing the square, and the quadratic formula. A quadratic equation is of the form ax^2 + bx + c = 0. Completing the square is a method used to solve this equation. The quadratic formula is another method to solve this equation, and is actually derivative from completing the square.
2Step 2: Evaluate the Statement
The statement says that any quadratic equation that can be solved by completing the square can also be solved by the quadratic formula. Since the quadratic formula is derived from the process of completing the square, it means that if a quadratic equation can be solved by completing the square, then it can also be solved using the quadratic formula.
3Step 3: Conclude the Statement
Therefore, the statement is True. Every quadratic equation that can be solved by completing the square can be solved using the quadratic formula.
Other exercises in this chapter
Problem 169
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I use the square root property to determine the length of
View solution Problem 170
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{
View solution Problem 172
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
View solution Problem 174
Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).
View solution