Home
Class 12
MATHS
The root of (x-a)(x-a-1)+(x-a-1)(x-a-2)+...

The root of `(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0, a in R` are always

A

equal

B

imaginary

C

real and distinct

D

rational and equal

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES OF TRIANGLES, HEIGHTS AND DISTANCES

    SIA PUBLICATION|Exercise Problems|54 Videos
  • QUESTION PAPER

    SIA PUBLICATION|Exercise CHEMISTRY|8 Videos

Similar Questions

Explore conceptually related problems

The roots of (7x-1)(2x+3)=0.

The roots of 5x^(2) - x + 1 = 0 are

The roots of 2x^(2) - x + 1/8 = 0 are…

The roots of the Q.E. (7x - 1)(2x + 3) = 0 are

The roots of x^(4) + 4x^(3) + 5x^(2) + 2x - 2 = 0 one root being -1 + i are

If the roots of 24x^(3) - 26x^(2) + 9x -1 = 0 are in H.P . Then the roots are

If k in R , then roots of (x - 2) (x - 3) = k^2 are always

SIA PUBLICATION-QUADRATIC EXPRESSIONS AND THEORY OF EQUATIONS -Problems
  1. The condition that the roots of x^(3)-bx^(2)+cx-d=0 are in geometric ...

    Text Solution

    |

  2. Let alpha !=1 be a real root of the equation x^(3)-ax^(2)+ax-1=0, whe...

    Text Solution

    |

  3. The root of (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0, a in R are alw...

    Text Solution

    |

  4. Let f(x)=x^(2)+ax+b, where a, b in R. If f(x)=0 has all its roots imag...

    Text Solution

    |

  5. If alpha, beta , gamma are the roots of x^(3)+4x+1=0, then the equatio...

    Text Solution

    |

  6. If f(x)=2x^(4)-13x^(2)+ax+b is divisible by x^(2)-3x+2, then (a, b) is...

    Text Solution

    |

  7. If alpha and beta are the roots of x^(2)-2x+4=0, then the value of alp...

    Text Solution

    |

  8. Let alpha and beta be the roots of quadratic equation ax^(2)+bx+c=0. M...

    Text Solution

    |

  9. IF alpha + beta =- 2 and alpha ^3 + beta ^3 =- 56 , then the ...

    Text Solution

    |

  10. The cubic equation, whose roots are thrice to each of the roots of x^(...

    Text Solution

    |

  11. The sum of the fourth powers of the roots of the equation x^(3)+x+1=0 ...

    Text Solution

    |

  12. If alpha and beta are roots of the equation ax^(2)+bx+c=0 and if px^(...

    Text Solution

    |

  13. The set of values of x for which the inequalities x^(2)-3x-10 lt 0, 1...

    Text Solution

    |

  14. If 1, 2, 3 and 4 are the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+...

    Text Solution

    |

  15. If alpha, beta, gamma are roots of x^(3) - 2x^(2) + 3x - 4 = 0, then t...

    Text Solution

    |

  16. A quadratic equation whose roots are sin^(2) 18^(@) , cos^(2) 36^(@) ...

    Text Solution

    |

  17. If sqrt(9x^(2)+6x+1) lt 2-x, then

    Text Solution

    |

  18. The difference between two roots of the equation x^(3)-13x^(2)+15x+189...

    Text Solution

    |

  19. If alpha, beta ,gamma are the roots of the equation x^(3)-6x^(2)+11x+6...

    Text Solution

    |

  20. The condition that sin theta cos theta may be the roots o...

    Text Solution

    |