Find the solutions for the following quadratic equations. Check by substituting your answers back into the original equations.
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1. (x + 3)(x − 4) = 0 |
12. a2 − 36 = 0 |
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2. (y − 6)(y + 2) = 0 |
13. |
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3. (z − 3)(z − 7) = 0 |
14. (b + 3)2 = 0 |
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4. p 2 + 4p − 12 = 0 |
15. (x − 2)2 = 0 |
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5. q 2 + 10q + 21 = 0 |
16. (2r + 5)(r − 1) = 0 |
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6. r 2 − 5r + 6 = 0 |
17. (3s − 4)(2s − 1) = 0 |
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7. x(x − 3) = 0 |
18. 2t 2 − 11t + 12 = 0 |
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8. 5y(y − 2) = 0 |
19. (x + 3)2 = 16 |
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9. 3y(2y − 5) = 0 |
20. x 2 − 4x = 12 |
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10. (x − 5)(x + 5) = 0 |
21. x 2 = 3x + 4 |
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11. (c + 2)(c − 2) = 0 |
22. (x − 2)2 − 9 = 0 |
For questions 23 to 25 make up a quadratic equation to help solve the problems.
23. A farmer's rectangular paddock is 10m longer than it is wide. Its area is 1200 m2. Find its length and width.
x
x + 10
24. The width of a painting is 10 cm less than its length. The area of the painting is 7200 cm2. Find the length and width of the painting.
25. A box is 12 cm high. Its volume is 1800 cm3. Its length is 5 cm more than its width. Find its length and width.
