Test questions for solving quadratic equations by taking square roots

📚 Quick Study Guide

• 🔢 When solving quadratic equations by taking square roots, isolate the squared term on one side of the equation.
• 💡 The general form to aim for is $x^2 = k$ or $(ax + b)^2 = k$, where $k$ is a constant.
• ➕ If $k > 0$, there are two real solutions: $x = \pm \sqrt{k}$.
• ➖ If $k = 0$, there is one real solution: $x = 0$.
• ⛔ If $k < 0$, there are no real solutions. The solutions are imaginary.
• ➗ For equations like $(ax + b)^2 = k$, take the square root of both sides, remembering both positive and negative roots: $ax + b = \pm \sqrt{k}$.
• 📝 Solve for $x$ in both cases (positive and negative) to find both solutions.

🧪 Practice Quiz

1. What are the solutions to the equation $x^2 = 25$?
   1. $x = 5$
   2. $x = -5$
   3. $x = 5, x = -5$
   4. No real solutions
2. Solve for $x$: $x^2 - 9 = 0$
   1. $x = 3$
   2. $x = -3$
   3. $x = 9$
   4. $x = 3, x = -3$
3. What are the solutions to $(x + 2)^2 = 16$?
   1. $x = 2, x = -6$
   2. $x = 6, x = -2$
   3. $x = 14, x = -18$
   4. $x = 2$
4. Find the value(s) of $x$ for which $4x^2 = 36$.
   1. $x = 3$
   2. $x = -3$
   3. $x = 9$
   4. $x = 3, x = -3$
5. Solve: $(2x - 1)^2 = 9$
   1. $x = 2, x = -1$
   2. $x = 5, x = -4$
   3. $x = 4, x = -5$
   4. $x = 1, x = -2$
6. What is the solution to $x^2 + 4 = 4$?
   1. $x = 4$
   2. $x = -4$
   3. $x = 0$
   4. No real solution
7. Solve: $(x - 3)^2 = 0$
   1. $x = 3$
   2. $x = -3$
   3. $x = 0$
   4. No solution