Home
Class 12
MATHS
Show that x^5 - 5x ^3 + 5x ^2 -1=0 ...

Show that `x^5 - 5x ^3 + 5x ^2 -1=0` has three equal roots and find this root.

Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXAMPLES|5 Videos

  • THEORY OF EQUATIONS

    AAKASH SERIES|Exercise EXERCISE -2.1 (VERY SHORT ANSWER QUESTIONS)|18 Videos

  • SYSTEM OF CIRCLES

    AAKASH SERIES|Exercise EXERCISE 2.2|22 Videos

  • TRANSFORMATIONS AND INDENTITIES

    AAKASH SERIES|Exercise PRACTIVE EXERCISE|36 Videos

Similar Questions

Explore conceptually related problems

The equation x^(5)-5x^(3)+5x^(2)-1=0 has three equal roots. If alpha,beta are the other two roots of this equation, then alpha+beta+alphabeta=

If -1 +i is a root of x^4 + 4x^3 + 5x^2 + k=0 then its real roots are

If the equation x^5 -3x^4 -5x^3 +27 x^2 - 32 x +12=0 has repeated roots , then the prime number that divides the non repeated root of this equation is

If the product of two of the roots of x^4 - 5x^3 + 5x^2 + 5x -6=0 is 2 then the roots are

If x^(4) -5x^(3) + 9x^(2) - 7x + 2 = 0 has a multiple roots of order 3 then the roots are

If 5x^(2) - kx + 11 = 0 has a root x = 3, then k =

The roots of 6x^(4) - 5x^(3) - 38x^(2) - 5x + 6 = 0 are

AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE-III
  1. Show that x^5 - 5x ^3 + 5x ^2 -1=0 has three equal roots and ...

    Text Solution

    |

  2. The quotient obtained when 3x^4 -x^3 +2x^2 -2x -4 is divided by ...

    Text Solution

    |

  3. The value of k so that x^4 -4x^3 +5x^2 -2x +k is divisible by ...

    Text Solution

    |

  4. The equation whose roots are 1,2 +- 3i is

    Text Solution

    |

  5. The polynomial equation of the lowest degree having roots 1 , ...

    Text Solution

    |

  6. The equation of lowest degree with rational coefficient having ...

    Text Solution

    |

  7. If one root of x^3 -6x^2 +3x +10 =0 is 2 then the remaining t...

    Text Solution

    |

  8. If one root of 10 x^3 -x^2 - 278 x + 165=0 is 5 then product ...

    Text Solution

    |

  9. If the product of two of the roots of x^3 +kx ^2 -3x+4=0 is -1 ...

    Text Solution

    |

  10. The condition for one root of x^3+ax^2+bx+c=0 is sum of the ot...

    Text Solution

    |

  11. If one of the roots of 18x^3 + 81x^2 + 121 x+60=0 is equal to ...

    Text Solution

    |

  12. If the roots of the equation x^3 -9x^2 + 23x-15=0 are in A.P t...

    Text Solution

    |

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

    Text Solution

    |

  14. If alpha , beta , gamma are the roots of x^3 -3ax^2 +3 bx -c=0...

    Text Solution

    |

  15. If the root of kx^3 - 18x^2 - 36 x+8=0 are in H.P then k=

    Text Solution

    |

  16. If the roots of x^3 -14x^2 + 56x-64 =0 are in G.P then the mid...

    Text Solution

    |

  17. If x^4 - 12x ^3 +52 x^2 - 96 x+64=0 have pairs of equal roots t...

    Text Solution

    |

  18. If the roots of x^4 -2x^3 - 21x^2 + 22 x + 40 =0 are in A.P then...

    Text Solution

    |

  19. If the roots of 27x^(4) - 195x^(3) + 494x^(2) - 520x + 192 = 0 are in...

    Text Solution

    |

  20. The roots of x^3 - 13x^2 +39 x-27=0 are in

    Text Solution

    |

  21. If x^3 -3x^2 + 4=0 has a multiple root then that multiple root i...

    Text Solution

    |