Home
Class 11
MATHS
Let alpha+ibeta;alpha,beta in R , be a ...

Let `alpha+ibeta;alpha,beta in R ,` be a root of the equation `x^3+q x+r=0; q ,r in Rdot` A real cubic equation, independent of `alpha&beta,` whose one root is `2alpha` is (a)`x^3+q x-r=0` (b) `x^3-q x+4=0` (c)`x^3+2q x+r=0` (d) None of these

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

IF alpha and beta be the roots of the equation x^2+3x+4=0 , find the equation whose roots are (alpha+beta)^2 and (alpha+beta)^2

If alpha,beta be the two roots of the equation x^2+x+1 =0, then the equation whose roots are alpha/beta and beta/alpha is

If alpha and beta be the roots of the equation x^2+3x+4=0 find the equation whose roots are (alpha+beta)^2 and (alpha-beta)^2 .

If alpha and beta are the roots of the equation x^2 + x + 1=0 , then me equation whose roots are alpha^(19) and beta^(7) is:

Let alpha,beta be the equation x^2-px+r=0 and alpha/2,2beta be the roots of the equation x^2-qx+r=0. Then, the value of r is

IF alpha and beta be the roots of the equation 2x^2+x+1=0 find the equation whose roots are alpha^2/beta and beta^2/alpha

If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the equation whose roots are alpha^2+2 and beta^2+2.

-alpha^2/beta and -beta^2/alpha are the roots of the equation 3x^2-18x+2=0 . Find the equation whose roots are alpha and beta ( alpha,beta real).

IF alpha,beta be the roots of the equation px^2+qx+r=0 ,find the value of 1/(palpha+q)^3+1/(pbeta+q)^3 .

If alpha and beta are the roots of the equation x^2+x+1=0 , then the equation whose roots are alpha^19 and beta^7 is

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the number of integal values of x satisfying sqrt(-x^2+10x-16)...

    Text Solution

    |

  2. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  3. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  4. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in magn...

    Text Solution

    |

  5. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

    Text Solution

    |

  6. The equation x^3+5x^2+px+q=0 and x^3+7x^2+px+r=0 have two roots in com...

    Text Solution

    |

  7. If alpha,beta,gamma are the roots of he euation x^3+4x+1=0, then find ...

    Text Solution

    |

  8. If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that...

    Text Solution

    |

  9. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

    Text Solution

    |

  10. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1...

    Text Solution

    |

  11. a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0and d...

    Text Solution

    |

  12. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

    Text Solution

    |

  13. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

    Text Solution

    |

  14. Solve (x^2+2)^2+8x^2=6x(x^2+2)

    Text Solution

    |

  15. Find the value of 2+1/(2+1/(2+1/(2+oo)))

    Text Solution

    |

  16. If both the roots of a x^2+a x+1=0 are less than 1, then find the exha...

    Text Solution

    |

  17. If both the roots of x^2+a x+2=0 lies in the interval (0, 3), then fin...

    Text Solution

    |

  18. Solve (x^2+3x+2)/(x^2-6x-7)=0.

    Text Solution

    |

  19. Solve sqrt(x-2)+sqrt(4-x)=2.

    Text Solution

    |

  20. Solve sqrt(x-2)(x^2-4x-5)=0.

    Text Solution

    |