Solving equations with surds

12 questions

1. Solve the equation 3(x+12) = 36
2. Solve the equation 2(3x - 10) - 3(7 - 5x) = 484
3. x^{2} + 2bx + c = (x + b)^{2} - b^{2} + c is known as completing the ___ .
4. Select the correct form for the quadratic formula.
5. Simplify the expression: \sqrt {12} \times \sqrt {30}
6. \sqrt {54} \times \sqrt {24}
7. Solve x\sqrt {180} - 30 = x\sqrt {80} and write your answer in the form a\sqrt {b}. State the value of b.
8. Solve x\sqrt {180} - 30 = x\sqrt {80} and write your answer in the form a\sqrt {b}. State the value of a.
9. True or false? The solutions to 2x^{2} + 9x - 2 = 0 are x = -9 \pm \sqrt {97}
10. Match the equation to its solutions
11. True or false? The solutions to x^{2} + 5x - 4 = 0 are x = \frac{1}{2} (-5 \pm \sqrt {41})
12. Is this statement true or false? "There are always two solutions to a quadratic equation"

License: OGL