Home
Class 12
MATHS
Let a= e^(i(2pi)/(3)). Then the equation...

Let `a= e^(i(2pi)/(3))`. Then the equation whose roots are `a+a^(-2)" and "a^(2)+a^(-4)` is

A

`x^(2)-2x+4=0`

B

`x^(2)-x+1=0`

C

`x^(2)+x+4=0`

D

`x^(2)+2x+4=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta are the roots of the equation x^(2)+x+1=0 , then the equation whose roots are alpha^(22)" and "beta^(19) , is

The equation whose roots are 1+sqrt2i and 1-sqrt2i is :

The roots of the equation x^(2)+6x-4=0 are alpha, beta . Find the quadratic equation whose roots area alpha^(2) and beta^(2)

IF alpha and beta are the roots of the equation 3x^(2)-4x+1=0 , form the equation whose roots are alpha^(2)/beta and beta^(2)/alpha.

If 3p^(2)=5p+2" and "3q^(2)= 5q+2 , where p ne q , then the equation whose roots are 3p-2q" and "3q-2p is

If 3p^(2)=5p+2" and "3q^(2)= 5q+2 , where p ne q , then the equation whose roots are 3p-2q" and "3q-2p is

If alpha and beta are the roots of 2x^2-5x+3=0 form the equation whose roots are alpha^2 and beta^2

(a) Solve (2x+1)^(2)-(3x+2)^(2)=0 (b) If alpha and beta are the roots of the equation 3x^(2)-4x+1=0 form the equation whose roots are (alpha^(2))/(beta^(2)) and (beta^(2))/(alpha^(2)) .

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. The solution set of the equation pqx^(2)-(p+q)^(2)x+(p+q)^(2)=0 is

    Text Solution

    |

  2. If roots alpha, beta of the equation (x^(2)-bx)/(ax-c)=(lambda-1)/(lam...

    Text Solution

    |

  3. Let a= e^(i(2pi)/(3)). Then the equation whose roots are a+a^(-2)" and...

    Text Solution

    |

  4. If alpha(1), alpha(2), alpha(3), alpha(4) are the roots of the equatio...

    Text Solution

    |

  5. The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

    Text Solution

    |

  6. Let omega be a imaginary root of x^(n)=1. Then (5- omega)(5- omega^2)"...

    Text Solution

    |

  7. If isqrt(-1), then 4+5(-(1)/(2)+(isqrt(3))/(2))^(334)+3(-(1)/(2)+(isqr...

    Text Solution

    |

  8. If z is a complex number such that Re(z)=Im(z), then

    Text Solution

    |

  9. If alpha" and "beta are the roots of the equation x^(2)-7x+1=0, then t...

    Text Solution

    |

  10. If alpha " and "beta are different complex numbers with |beta|=1, then...

    Text Solution

    |

  11. If omega is a complex cube root of unity, then the value of sin{(omega...

    Text Solution

    |

  12. Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, ...

    Text Solution

    |

  13. Let z(1)" and "z(2) be the roots of the equation z^(2)+pz+q=0, where p...

    Text Solution

    |

  14. If alpha, beta, gamma are the cube roots of a negative number p, then ...

    Text Solution

    |

  15. The magnitude and amplitude of ((1+isqrt(3))(2+2i))/((sqrt(3)-i)) are ...

    Text Solution

    |

  16. If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^n))^(2) is equal ...

    Text Solution

    |

  17. If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then (a...

    Text Solution

    |

  18. If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(...

    Text Solution

    |

  19. Given tan A and tan B are the roots of x^(2)-ax+b=0. The value of sin^...

    Text Solution

    |

  20. The number of roots of the equation |x|= x^(2)+x-4 is

    Text Solution

    |