Home
Class 11
MATHS
If the roots of the equation : a(b - c)...

If the roots of the equation : `a(b - c)x^2 +b (c - a)x + c(a - b) = 0 ` are equal, show that `1/a,1/b,1/c` are in A.P.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If a,b,c are in A.P. then :

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

If a+b+c ne 0 and (b + c)/a, (c + a)/b, (a + b)/c are in A.P., prove that : 1/a,1/b,1/c are also in A.P.

If a, b,c be the sides of a triangle ABC and if roots of equation a(b-c)x^2+b(c-a)x+c(a-b)=90 are equal then sin^2 A/2, sin^2 B/2, sin^2 C/2 are in

If a(1/b +1/c) , b(1/c +1/a), c(1/a + 1/b) are in A.P. Prove that a,b,c are in A.P.

Which one of the following is one of the roots of the equation (b-c) x^2 + (c-a)x+(a-b)=0 ?

If a, b, c are real, then both the roots of the equation : (x- b) (x-c) + (x-c) (x-a) + (x-a)(x-b) are always :

If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P, prove that a, b, c are in A.P.

If the sum of the roots of ax^2bx +c = 0 is equal to the sum of the squares of their reciprocals, then show that c/a, a/b, b/c are in A.P.

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. If the roots of the equation : a(b - c)x^2 +b (c - a)x + c(a - b) = 0...

    Text Solution

    |

  2. Write the first three terms of the sequence defined by the following :...

    Text Solution

    |

  3. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  4. Write the first five terms of the following functions whose nth terms ...

    Text Solution

    |

  5. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  6. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  7. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  8. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  9. Write the first four terms of the following sequence whose nth terms a...

    Text Solution

    |

  10. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  11. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  12. Write the first five terms of the following sequence whose nth terms a...

    Text Solution

    |

  13. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  14. Write the first five terms of the sequences given below whose nth term...

    Text Solution

    |

  15. What is the 19th term of the sequence : a(n) = (n(n-2))/(n+3)?

    Text Solution

    |

  16. Find the term indicated in the following case : t(n)=4^(n)+n^(2)-n+1...

    Text Solution

    |

  17. Find the term indicated in the following case : h(n)=n^(2)-3n+4, h(1...

    Text Solution

    |

  18. Find the term indicated in the following case : an= n^2/2^n , a7.

    Text Solution

    |

  19. Find the term indicated in the following case : an= (-1)^(n-1) n^3 ,...

    Text Solution

    |

  20. Find the term indicated in the following case : an= (n(n-2))/(n-3), ...

    Text Solution

    |

  21. Find the first five terms of the sequence and write corresponding seri...

    Text Solution

    |