Home
Class 12
MATHS
If x^(2)+x+1 is a factor of a x^(3)+b x^...

If `x^(2)+x+1` is a factor of a `x^(3)+b x^(2)+c x+d`, then the real root of `a x^(3)+b x^(2)+c x+d=0` is

A

`(d)/(a)`

B

`-(d)/(a)`

C

`-(b)/(a)`

D

` -(c)/(a)`.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos
  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then

If x - 1 is a factor of x^(5) - 4x^(3) +2 x^(2) - 3x + k = 0 then k is

The real roots of | x|^(3) - 3x^(2) + 3 | x| - 2 = 0 are :

If a,b are the roots of x^(3)-5x^(2)-x+5=0 b is a root of

If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a root in

The number of real roots of the equation |x|^(2)-3|x|+2=0 is

If a, b,c , d are the roots of the equation : x^(4) + 2x^(3) + 3x^(2) + 4x + 5 = 0 , then 1 + a^(2) + b^(2) + c^(2) + d^(2) is equal to :

If a, b, c are positive real numbers, then the number of real roots of the equation a x^(2)+b|x|+c=0 is

If a le b le c le d then the equation (x-a)(x-c)+2(x-b)(x-d)=0 has

If the ratio of the roots of a_(1)x^(2) + b_(1) x + c_(1) = 0 be equal to the ratio of the roots of a_(2) x^(2) + b_(2)x + c_(2) = 0 , then (a_(1))/(a_(2)) , (b_(1))/(b_(2)) , (c_(1))/(c_(2)) are in :

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. If a, b, c are positive real numbers, then the number of real roots of...

    Text Solution

    |

  2. The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) +...

    Text Solution

    |

  3. If alpha and beta are the roots of x^(2) + qx + 1 = 0 and gamma, delt...

    Text Solution

    |

  4. If a,b,c are in G.P.L, then the equations ax^(2) + 2bx + c = 0 0 and d...

    Text Solution

    |

  5. Let x(1), x(2) be the roots of the equation x^(2)-3 x+p=0 and let x(3)...

    Text Solution

    |

  6. Both the roots of the equation : (x - b) (x -c) + (x - c) (x - a) +...

    Text Solution

    |

  7. If x^(2)+x+1 is a factor of a x^(3)+b x^(2)+c x+d, then the real root ...

    Text Solution

    |

  8. If a le 0 then the real values of x satisfying x^(2)-2 a|x-a|-3 a^(2)=...

    Text Solution

    |

  9. If x^(2)-3 x+2 is a factor of x^(4)-p x^(2)+q, then the values of p an...

    Text Solution

    |

  10. If the equations x^(2)+b^(2)=1-2b x and x^(2)+a^(2)=1-2 a x have one a...

    Text Solution

    |

  11. If the product of the roots of the equation x^(2) - 3kx + 2e^(2 log k)...

    Text Solution

    |

  12. Let a, b, c be real. If a x^(2)+b x+c=0 has two real roots alpha and...

    Text Solution

    |

  13. Let (sin a) x^(2)+(sin a) x+(1-cos a)=0 . The set of values of a for w...

    Text Solution

    |

  14. If p, q, are real and p ne q then the roots of the equation (p-q) x^(...

    Text Solution

    |

  15. The value of ' c ' for which |alpha^(2)-beta^(2)|=(7)/(4) where alpha ...

    Text Solution

    |

  16. If alpha, beta are the roots of the equation λ (x^(2)-x)+x+5=0 and if ...

    Text Solution

    |

  17. If alpha and beta are the rotos of a x^(2)+b x+c=0 the equation whose ...

    Text Solution

    |

  18. If alpha, beta are the rots of a x^(2)+b x+c=0 and alpha+h, beta+h are...

    Text Solution

    |

  19. If x^(2) + ax + b = 0 and x^(2) + bx + a = 0 have a common root, then...

    Text Solution

    |

  20. The minimum value of 2 x^(2)+x-1 is

    Text Solution

    |