Home
Class 12
MATHS
Let alpha+ibeta,alpha, beta epsilon R, b...

Let `alpha+ibeta,alpha, beta epsilon R`, be a root of the equation `x^(3)+qx+r=0p,q,r epsilonR`. Find a real cubic equation, independent of `alpha` and `beta`, whose one root `2 alpha`.

Text Solution

Verified by Experts

The correct Answer is:
`x^(3)+qx-r=0`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -2 (MCQ)|9 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

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

If alpha,beta be the roots of the equation x^(2)-px+q=0 then find the equation whose roots are (q)/(p-alpha) and (q)/(p-beta)

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0 such that alpha+beta=0 then

If alpha,beta,gamma are the roots of the equation x^(3)-px+q=0, ten find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma)

If alpha and beta are roots of the equation x^2 – x-1 = 0 , then the equation where roots are alpha/beta and beta/alpha is:

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

If alpha,beta,gamma are the roots of the equation x^(3)-px^(2)+qx-r=0 then the value of sum alpha^(2)beta=

MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + ...

    Text Solution

    |

  2. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

    Text Solution

    |

  3. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

    Text Solution

    |

  4. Let alpha,beta,gamma are the roots of the cubic x^3-3x^2+1=0 .Find a c...

    Text Solution

    |

  5. Two roots of a biquadratic x^4-18x^3+ kx^2+ 200x-1984=0 have their pro...

    Text Solution

    |

  6. Suppose a cubic polynomial f(x) = x^3 + px^2 + qx + 72 is divisible by...

    Text Solution

    |

  7. If g(x)=x^(3)+px^(2)+qx+r where p,q,r are integers. If g(0) and g(-1)...

    Text Solution

    |

  8. If x be real then find the range of the following rational expressions...

    Text Solution

    |

  9. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  10. Find the range of values of a, such that f(x)=(ax^2+2(a+1)x+9a+4)/(x^2...

    Text Solution

    |

  11. The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2)...

    Text Solution

    |

  12. Find all real numbers x such that (x-1/x)^(1/2)+(1-1/x)^(1/2)=x

    Text Solution

    |

  13. The minimum value of ((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^...

    Text Solution

    |

  14. Find the product of the real roots of the equation, x^2+18x +30=2sqrt(...

    Text Solution

    |

  15. The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...

    Text Solution

    |

  16. Find all the values of the parameters c for which the inequality has a...

    Text Solution

    |

  17. Find the complete set of real values of a for which both roots of the ...

    Text Solution

    |

  18. Let p(x) = x^2+bx+c, where b and c are integers. If p(x) is a factor o...

    Text Solution

    |

  19. Find the value of k for which one root of the equation of x^(2)-(k+1)x...

    Text Solution

    |

  20. If the roots of x^2-ax+b=0 are real and differ by a quantity which is ...

    Text Solution

    |