📚 Topic Summary
Solving quadratic equations by square roots is a method used when the equation is in a specific form, primarily when there's no 'x' term (just an $x^2$ term, a constant, and potentially a coefficient in front of $x^2$). The goal is to isolate the $x^2$ term on one side of the equation and then take the square root of both sides. Remember that when you take the square root, you get both a positive and a negative solution!
This method is efficient because it directly undoes the squaring operation. However, it only works for quadratic equations that can be rearranged into the form $ax^2 + c = 0$, where 'a' and 'c' are constants. For other types of quadratic equations, you'll need to use factoring, completing the square, or the quadratic formula.
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Quadratic Equation |
A. The number that, when multiplied by itself, equals a given number. |
| 2. Square Root |
B. A term without any variables. |
| 3. Constant |
C. A value that, when squared, equals a non-negative real number. |
| 4. Real Number |
D. An equation in the form $ax^2 + bx + c = 0$, where a ≠ 0. |
| 5. Isolate |
E. To separate a variable on one side of an equation. |
Match the numbers to the letters.
✍️ Part B: Fill in the Blanks
Complete the paragraph using the words: square root, positive, negative, isolate, quadratic.
To solve a simple ______ equation by ______, we first need to ______ the $x^2$ term. After isolating, we take the square root of both sides of the equation. Remember that the solution includes both a ______ and a ______ value.
🤔 Part C: Critical Thinking
Explain why solving a quadratic equation by square roots results in both a positive and a negative solution. Give an example.