11X1 T10 05 the discriminant (2010)

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  • 1. The Discriminant

2. The Discriminant b 2 4ac 3. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 4. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 5. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 6. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) 7. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rational 8. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; 9. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0 10. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0 52 4 3 9 83 0 11. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0 52 4 3 9 83 0 no real roots 12. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0b ) 2x 2 6 x 3 0 52 4 3 9 83 0 no real roots 13. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0b ) 2x 2 6 x 3 0 52 4 3 9 62 4 2 3 83 0 60 0 no real roots 14. The Discriminant b 2 4acThe discriminant tells us whether the roots are rational or irrational 0 : two different real roots (cuts the x axis twice) 0 : two equal real roots (touches the x axis once) 0 : no real roots (never touches the x axis) is a perfect square : roots are rationale.g. (i ) Describe the roots of; a) 3x 2 5 x 9 0b ) 2x 2 6 x 3 0 52 4 3 9 62 4 2 3 83 0 60 0 no real roots two different, real, irrational roots 15. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal roots 16. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0 17. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 18. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 36 4k 0 k 9 19. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 36 4k 0 k 9b) x 2 4 x 2k 0 have unreal roots 20. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 36 4k 0 k 9b) x 2 4 x 2k 0 have unreal rootsunreal roots occur when 0 21. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 36 4k 0 k 9b) x 2 4 x 2k 0 have unreal rootsunreal roots occur when 0i.e. 4 4 2k 0 2 22. (ii) Find the values of k which makes;a ) x 2 6 x k 0 have equal rootsequal roots occur when 0i.e. 62 4k 0 36 4k 0 k 9b) x 2 4 x 2k 0 have unreal rootsunreal roots occur when 0i.e. 4 4 2k 0 2 16 8k 0 k 2 23. c) kx 2 2 x 4k 0 have real roots 24. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 25. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 0 26. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 0 4 16k 2 0 1 k 24 27. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 0 4 16k 2 0 1 k 2411 k22 28. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 04 16k 2 01k 2 4 11 k 22(iii ) For what value of a is the line y ax a tangent tothe circle x 2 y 2 20 x 10 y 100 0? 29. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 04 16k 2 01k 2 4 11 k 22(iii ) For what value of a is the line y ax a tangent tothe circle x 2 y 2 20 x 10 y 100 0?x 2 a 2 x 2 20 x 10ax 100 0 30. c) kx 2 2 x 4k 0 have real rootsreal roots occur when 0 i.e. 22 4 k 4k 04 16k 2 01k 2 4 11 k 22(iii ) For what value of a is the line y ax a tangent tothe circle x 2 y 2 20 x 10 y 100 0?x 2 a 2 x 2 20 x 10ax 100 0a 2 1 x 2 10 2 a x 100 0 31. line is a tangent when 0 32. line is a tangent when 0 i.e. 100 2 a 4 a 2 1 100 02 33. line is a tangent when 0i.e. 100 2 a 4 a 2 1 100 0 2 400 400a 100a 2 400a 2 400 0 34. line is a tangent when 0i.e. 100 2 a 4 a 2 1 100 0 2 400 400a 100a 2 400a 2 400 0 3a 2 4a 0 35. line is a tangent when 0i.e. 100 2 a 4 a 2 1 100 0 2 400 400a 100a 2 400a 2 400 0 3a 2 4a 0a 3a 4 0 36. line is a tangent when 0i.e. 100 2 a 4 a 2 1 100 0 2 400 400a 100a 2 400a 2 400 0 3a 2 4a 0a 3a 4 0 4 a0 or a 3 37. line is a tangent when 0 i.e. 100 2 a 4 a 2 1 100 02400 400a 100a 2 400a 2 400 03a 2 4a 0 a 3a 4 04a0 or a 3 Exercise 8F; 1ace, 2bdf, 3bg, 4ch, 5ad, 6, 7ac, 8be, 9ac,11, 12b, 13, 14, 18, 21bd