מתמטיקה תיכונית/אלגברה תיכונית/משוואות/משוואות ריבועיות/תרגילים/נוסחת השורשים ג

נוסחת השורשים - תרגילים

פתרו את המשוואות הבאות בעזרת נוסחת השורשים, או בכל דרך אחרת. מותר להשתמש במחשבון.

1. $5x^{2}-5x-{\frac {2929}{12}}=-{\frac {1}{3}}$
2. ${\frac {25}{13}}x^{2}-{\frac {47}{60}}x-{\frac {306}{11}}={\frac {12}{13}}x^{2}-{\frac {13}{4}}x+{\frac {2}{11}}$
3. $5x^{2}+{\frac {123}{2}}x-{\frac {1615}{2}}=9x$
4. ${\frac {1}{4}}x^{2}+{\frac {149}{22}}x-{\frac {161}{3}}=-{\frac {3}{4}}x^{2}-{\frac {8}{11}}x+{\frac {1}{3}}$
5. $5x^{2}-{\frac {275}{21}}x-{\frac {2649}{70}}=-{\frac {7}{10}}$
6. $7x^{2}+{\frac {105}{4}}x+{\frac {763}{52}}=-{\frac {14}{13}}$
7. $3x^{2}+{\frac {1}{5}}x-41=-{\frac {7}{5}}$
8. $x^{2}+{\frac {1}{2}}x-{\frac {103}{9}}=-2$
9. $6x^{2}+{\frac {10134}{91}}x+{\frac {9813}{56}}=-{\frac {12}{13}}x+{\frac {3}{8}}$
10. $6x^{2}-{\frac {101}{7}}x+{\frac {148}{7}}=4x+7$
11. ${\frac {14}{5}}x^{2}+{\frac {743}{70}}x+{\frac {201}{40}}=-{\frac {6}{5}}x^{2}+{\frac {3}{14}}x-{\frac {11}{8}}$
12. $x^{2}+{\frac {33}{10}}x+{\frac {56}{15}}={\frac {7}{3}}$
13. $4x^{2}-{\frac {226}{5}}x+{\frac {486}{5}}=2$
14. $6x^{2}-{\frac {150}{7}}x+{\frac {285}{14}}={\frac {3}{2}}$
15. $3x^{2}+{\frac {303}{10}}x+{\frac {386}{5}}=7$
16. ${\frac {68}{11}}x^{2}+{\frac {769}{21}}x-{\frac {302}{11}}=-{\frac {9}{11}}x^{2}-{\frac {5}{7}}x+{\frac {6}{11}}$
17. $5x^{2}+{\frac {927}{28}}x+{\frac {393}{7}}=-{\frac {9}{14}}x+{\frac {8}{7}}$
18. ${\frac {49}{12}}x^{2}+{\frac {298}{63}}x-29={\frac {13}{12}}x^{2}+{\frac {13}{9}}x-{\frac {5}{7}}$
19. ${\frac {22}{7}}x^{2}-{\frac {73}{4}}x+{\frac {671}{40}}={\frac {1}{7}}x^{2}-x-{\frac {1}{10}}$
20. $3x^{2}+{\frac {40}{7}}x+{\frac {1203}{91}}=-8x-{\frac {12}{13}}$
21. $3x^{2}+{\frac {971}{12}}x+{\frac {1817}{4}}=-{\frac {1}{12}}x-{\frac {7}{4}}$
22. $7x^{2}-{\frac {581}{15}}x+{\frac {311}{6}}={\frac {1}{2}}$
23. $x^{2}+5x+{\frac {69}{20}}=-{\frac {9}{5}}$
24. $7x^{2}-14x-{\frac {59}{3}}={\frac {4}{3}}$
25. $x^{2}+{\frac {57}{14}}x+{\frac {29}{35}}={\frac {3}{14}}x+{\frac {7}{5}}$
26. $x^{2}-{\frac {1}{7}}x+{\frac {11}{14}}=-x+{\frac {11}{14}}$
27. $2x^{2}-52x+{\frac {1681}{5}}=-{\frac {9}{5}}$
28. ${\frac {25}{12}}x^{2}-{\frac {257}{35}}x-{\frac {22}{49}}={\frac {1}{12}}x^{2}-{\frac {1}{5}}x-6$
29. ${\frac {89}{13}}x^{2}+{\frac {33}{20}}x-{\frac {313}{65}}=-{\frac {2}{13}}x^{2}+2x-{\frac {8}{13}}$
30. $3x^{2}-{\frac {3}{4}}x-{\frac {311}{4}}=1$
31. $x^{2}-{\frac {19}{5}}x+{\frac {37}{5}}=5$
32. ${\frac {28}{11}}x^{2}+26x+{\frac {139}{7}}=-{\frac {5}{11}}x^{2}-{\frac {1}{4}}x+{\frac {13}{7}}$
33. $x^{2}-{\frac {220}{21}}x+{\frac {271}{21}}=-2x-{\frac {2}{3}}$
34. $3x^{2}+3x-{\frac {88}{13}}=-{\frac {10}{13}}$
35. $x^{2}+{\frac {463}{10}}x-{\frac {247}{5}}={\frac {13}{10}}x+{\frac {3}{5}}$
36. $2x^{2}-{\frac {1}{7}}x+{\frac {8}{11}}=x+{\frac {8}{11}}$
37. $x^{2}-{\frac {55}{3}}x+{\frac {328}{15}}=-{\frac {4}{5}}$
38. $x^{2}+{\frac {8}{5}}x-{\frac {2132}{225}}={\frac {13}{9}}$
39. ${\frac {7}{5}}x^{2}+{\frac {99}{7}}x-{\frac {122}{3}}=-{\frac {3}{5}}x^{2}-{\frac {13}{7}}x-{\frac {2}{3}}$
40. ${\frac {25}{9}}x^{2}+{\frac {106}{5}}x+{\frac {175}{4}}=-{\frac {2}{9}}x^{2}-{\frac {9}{5}}x+1$
41. $4x^{2}+{\frac {295}{14}}x-{\frac {146}{11}}=-{\frac {13}{14}}x-{\frac {14}{11}}$
42. $4x^{2}+8x+{\frac {181}{49}}=1$
43. $6x^{2}-72x+{\frac {793}{12}}={\frac {1}{12}}$
44. ${\frac {79}{11}}x^{2}-8x-{\frac {341}{5}}={\frac {13}{11}}x^{2}+4x-{\frac {7}{10}}$
45. $2x^{2}+{\frac {14}{3}}x-{\frac {10}{3}}=-x$
46. $6x^{2}+167x+{\frac {5684}{5}}=-13x+{\frac {14}{5}}$
47. $7x^{2}+{\frac {49}{2}}x+{\frac {133}{8}}=-{\frac {7}{8}}$
48. $5x^{2}+{\frac {25}{14}}x-{\frac {233}{182}}=-{\frac {12}{13}}$
49. $4x^{2}+48x+{\frac {5}{2}}={\frac {5}{2}}$
50. $7x^{2}-{\frac {161}{5}}x+{\frac {1933}{175}}=-{\frac {5}{7}}$

תשובות סופיות

1. $\left\{-{\frac {13}{2}},{\frac {15}{2}}\right\}$
2. $\left\{{\frac {21}{5}},-{\frac {20}{3}}\right\}$
3. $\left\{{\frac {17}{2}},-19\right\}$
4. $\left\{-12,{\frac {9}{2}}\right\}$
5. $\left\{{\frac {13}{3}},-{\frac {12}{7}}\right\}$
6. $\left\{-{\frac {3}{4}},-3\right\}$
7. $\left\{{\frac {18}{5}},-{\frac {11}{3}}\right\}$
8. $\left\{{\frac {17}{6}},-{\frac {10}{3}}\right\}$
9. $\left\{-{\frac {12}{7}},-17\right\}$
10. $\left\{{\frac {3}{2}},{\frac {11}{7}}\right\}$
11. $\left\{-{\frac {8}{5}},-1\right\}$
12. $\left\{-{\frac {1}{2}},-{\frac {14}{5}}\right\}$
13. $\left\{{\frac {14}{5}},{\frac {17}{2}}\right\}$
14. $\left\{2,{\frac {11}{7}}\right\}$
15. $\left\{-{\frac {13}{2}},-{\frac {18}{5}}\right\}$
16. $\left\{{\frac {2}{3}},-6\right\}$
17. $\left\{-{\frac {11}{4}},-4\right\}$
18. $\left\{{\frac {18}{7}},-{\frac {11}{3}}\right\}$
19. $\left\{{\frac {9}{2}},{\frac {5}{4}}\right\}$
20. $\left\{-{\frac {11}{7}},-3\right\}$
21. $\{-19,-8\}$
22. $\left\{{\frac {11}{5}},{\frac {10}{3}}\right\}$
23. $\left\{-{\frac {7}{2}},-{\frac {3}{2}}\right\}$
24. $\{-1,3\}$
25. $\left\{{\frac {1}{7}},-4\right\}$
26. $\left\{0,-{\frac {6}{7}}\right\}$
27. $\{13\}$
28. $\left\{{\frac {8}{7}},{\frac {17}{7}}\right\}$
29. $\left\{{\frac {4}{5}},-{\frac {3}{4}}\right\}$
30. $\left\{{\frac {21}{4}},-5\right\}$
31. $\left\{3,{\frac {4}{5}}\right\}$
32. $\left\{-{\frac {3}{4}},-8\right\}$
33. $\left\{{\frac {15}{7}},{\frac {19}{3}}\right\}$
34. $\{1,-2\}$
35. $\{-10,1\}$
36. $\left\{0,{\frac {4}{7}}\right\}$
37. $\left\{{\frac {4}{3}},17\right\}$
38. $\left\{{\frac {13}{5}},-{\frac {21}{5}}\right\}$
39. $\{-10,2\}$
40. $\left\{-{\frac {19}{6}},-{\frac {9}{2}}\right\}$
41. $\left\{{\frac {1}{2}},-6\right\}$
42. $\left\{-{\frac {3}{7}},-{\frac {11}{7}}\right\}$
43. $\{1,11\}$
44. $\left\{{\frac {9}{2}},-{\frac {5}{2}}\right\}$
45. $\left\{-{\frac {10}{3}},{\frac {1}{2}}\right\}$
46. $\{-21,-9\}$
47. $\left\{-{\frac {5}{2}},-1\right\}$
48. $\left\{-{\frac {1}{2}},{\frac {1}{7}}\right\}$
49. $\{0,-12\}$
50. $\left\{{\frac {21}{5}},{\frac {2}{5}}\right\}$