Home
Class 12
MATHS
If c ,d are the roots of the equation (x...

If `c ,d` are the roots of the equation `(x-a)(x-b)-k=0` , prove that a, b are roots of the equation `(x-c)(x-d)+k=0.`

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos
  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

Similar Questions

Explore conceptually related problems

If c,d are the roots of the equation (x-a)(x-b)-k=0, prove that a a,b are roots of the equation (x-c)(x-d)+k=0

If c and d are roots of the equation (x-a) (x-b) - k = 0, then a, b are roots of the equation

If m and n are roots of the equation (x+p)(x+q)-k=0 then find the roots of the equation (x-m)(x-n)+k=0

If alpha,beta be the roots of the equation (x-a)(x-b)+c=0(c!=0), then the roots of the equation (x-c-alpha)(x-c-beta)=c are a and b+c (b) a+b and ba+c and b+c(d)a-candb-c

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

If alpha and beta be the roots of the equation (x-a)(x-b)=c and c!=0 ,then roots of the equation (x-alpha)(x-beta)+c=0 are

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If alpha,beta be the roots of the equation lambda^2(x^2 - x) + 2lambda...

    Text Solution

    |

  2. If a, b are the roots of x^2 + px + 1 = 0 and c, d are the roots of ...

    Text Solution

    |

  3. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

    Text Solution

    |

  4. If alpha,beta are roots of x^2-px+q=0 then find the quadratic equation...

    Text Solution

    |

  5. The coefficient of x in the equation x^2+px+q=0 was wrongly written as...

    Text Solution

    |

  6. In copying a quadratic equation of the form x^2 +px +q=0,a student wro...

    Text Solution

    |

  7. Find p in R for which x^2-px+p+3=0 has one positive and one negative r...

    Text Solution

    |

  8. Find p in R for which x^2-px+p+3=0 has one root>2 and the other root<2...

    Text Solution

    |

  9. For what values of a inR, the quadratic equation (a^2+1)x -(a+l)x+( a^...

    Text Solution

    |

  10. For what values of a, does the equation ax^2 -(a + 1)x + 3 = 0, have r...

    Text Solution

    |

  11. Find the real values of the parameter a such that (2a + 1)x^2-a(x-1) =...

    Text Solution

    |

  12. Find the integral values of a for which the equation x^4-(a^2-5a+6)x^2...

    Text Solution

    |

  13. Find the values of k so that the quadratic equation x^2 + 2(k-1)x + k+...

    Text Solution

    |

  14. The range of real values of 'p' for which the equation 2log3^2 x-|log...

    Text Solution

    |

  15. For what values of the parameter a the equation x^(4)+2ax^(3)+x^(2)+2a...

    Text Solution

    |

  16. For what values of the parameter a the equation x^(4)+2ax^(3)+x^(2)+2a...

    Text Solution

    |

  17. Find the integral values of a for which (a+2)x^2+2(a+1)x+a=0 will have...

    Text Solution

    |

  18. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

    Text Solution

    |

  19. Find t values of the parameter a such that the rots alpha,beta of the ...

    Text Solution

    |

  20. If the roots of 10x^3-cx^2-54x -27 0 are in harmonic progression, then...

    Text Solution

    |