Home
Class 11
MATHS
If roots of the equation x^2-10cx-11d=0 ...

If roots of the equation `x^2-10cx-11d`=0 are a,b and those of `x^2-10ax-11b`=0 are c,d,then the sum of the digits of a+b+c+d must be equal to (a,b,c and d are distinct numbers)

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos
  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

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

If the equation x^2-cx+d=0 and x^2-ax+b=0 have a common root,and the roots of the second equations are equal ,then prove that 2(b+d)=ac

If the roots of the equation x^2+a x+b=0 are c and d , then roots of the equation x^2+(2c+a)x+c^2+a c+b=0 are a c b. d-c c. 2c d. 0

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If 1,2,3 and 4 are the roots of the equation x^4+ax^3+bx^2+cx+d =0 then a+2b+c=

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If 2 + i and sqrt5-2i are the roots of the equation (x^2+ax+b)(x^2+cx+d)=0 , where a,b,c,d are real constants, then product of all roots of the equation is

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.

If the roots of the quadratic equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 are equal, prove that a/b=c/d .

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. The smallest value of k, for which both roots of the equation x^2-8kx+...

    Text Solution

    |

  2. Let (x,y,z) be points with Integer coordinates satisfying the system o...

    Text Solution

    |

  3. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

  4. If alpha,beta,gamma are such that alpha+beta+gamma=4, alpha^2+beta^2+g...

    Text Solution

    |

  5. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  6. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  7. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  8. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  9. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  10. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  11. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  12. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  13. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  14. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  15. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  16. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  17. Find the values of the parameter a for which the roots of the quadrati...

    Text Solution

    |

  18. Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=...

    Text Solution

    |

  19. Solve the equation (x^2-6x)^2=81+2(x-3)^2

    Text Solution

    |

  20. abs(x^2-3x-4)=9-abs(x^2-1)

    Text Solution

    |