Quadratic Equations

1. Solve by factoring:  \(\displaystyle{ 3x^4 - 27x^2 = 0} \)    solution

2. Solve  \(\displaystyle{ \frac{x}{2x + 1} = \frac{3x + 2}{4x + 3}} \)    solution

3. Solve  \(\displaystyle{ \frac{6x - 7}{x} - \frac{8}{x^2} = 5 }\)    solution

4. Solve  \(\displaystyle{ \frac{3}{x + 3} + \frac{x}{x - 3} = \frac{6x}{x^2 - 9} }\)    solution

5. Solve  \(\displaystyle{ \frac{x}{x - 3} - \frac{1}{x + 2} = \frac{9}{x^2 - x -6} }\)    solution 

6. Solve each equation. Check your answer.    solution

(a)  \(\displaystyle{ \sqrt[3]{3x + 1}  = 4} \)        (b) \(\displaystyle{ \sqrt{2x - 3}  = -1} \)

7. Solve  \(\displaystyle{ \sqrt{6x + 4}  = x - 2} \)    solution

8. Solve  \(\displaystyle{ \sqrt{3y + 5} + 1 = y} \)    solution

9. Solve  \(\displaystyle{ \sqrt{2x - 5} - \sqrt{ x - 3} = 1} \)    solution

10. Solve  \(\displaystyle{ x^4 - 13x^2 + 36 = 0} \)    solution

11. Solve  \(\displaystyle{4p^4 - 3p^2 -1 = 0} \)    solution

12. Solve  \(\displaystyle{ x^{2/5} + x^{1/5} - 2 = 0} \)    solution  

13. Solve  \(\displaystyle{ 2 x^{1/2} -5 x^{1/4} - 3 = 0} \)    solution

14. Solve  \(\displaystyle{ x^{-2} + x^{-1} - 42 = 0} \)    solution 

15. Solve  \(\displaystyle{ (3x+1)^2 - 7(3x+1) + 6 = 0} \)   solution