Home
Class 12
MATHS
Assertion (A) : If alpha=cos((2pi)/(7))+...

Assertion (A) : If `alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^2+alpha^4,q=alpha^3+alpha^5+alpha^6` then the equation whose roots are p and q is `x^2+x+2=0`
Reason (R) : If `alpha` is a roots of `z^7=1` then `1+alpha+alpha^2+…...+alpha^6=0`

A

Both A and R are true R is correct explanation to A

B

Both A and R are true but R is not correct explanation to A

C

A is true R is false

D

A is false R is true

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE -II|58 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

If alpha is a non-real root of x^(7) = 1 then alpha (1 + alpha)(1 + alpha^(2) + alpha^(4))=

If alpha is a non-real root of x^(7) = 1 then alpha(1 + alpha) (1 + alpha^(2) + alpha^(4)) =

If alpha is a non real root of x^6=1 then (alpha^5+alpha^3+alpha+1)/(alpha^2+1)=

IF a = cos ( (2 pi ) /(7)) + isin ((2pi)/(7)) , alpha = a + a^2+a^4 and beta = a^3+a^5+a^6 then alpha , beta are the roots of the equation

If alpha , beta are the roots of 3x ^2 -5x+7=0 then alpha ^3 + beta ^3=

IF alpha^2=5alpha-6,beta^2=5beta-6, alpha ne beta then the equation whose roots alpha/beta,beta/alpha is……

If alpha = (2pi )/(7) , then tan alpha tan 2 alpha + tan 2 alpha tan 4 alpha + tan 4 alpha tan alpha =

IF alpha is a root of the equation 4x ^2 +2x-1=0 then 4 alpha ^3 - 3 alpha is

If alpha and beta are the roots of x^2-2x+3=0 then alpha^2beta+ beta^2 alpha =….

AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. 1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...

    Text Solution

    |

  2. If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, the...

    Text Solution

    |

  3. A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^...

    Text Solution

    |

  4. Assertion (A): If A, B, C are the angles of a triangle such that cos A...

    Text Solution

    |

  5. IF omega represents a complex cube root of unity, then (1+1/omega)(1+1...

    Text Solution

    |

  6. Assertion (A) : If alpha=cos((2pi)/(7))+isin((2pi)/(7)),p=alpha+alpha^...

    Text Solution

    |

  7. If z=(sqrt3-i)/(2) then (i^(101)+z^(101))^(103)=

    Text Solution

    |

  8. The roots of (z-1)^n=i(z+1)^n are plotted on the argand plane they are

    Text Solution

    |

  9. If 'alpha' be the non-real n^(th) roots of unity, then 1+3alpha+5alpha...

    Text Solution

    |

  10. If cos alpha+2cos beta+3cos gamma=sinalpha+2sinbeta+3singamma=0 then s...

    Text Solution

    |

  11. If sin(A+iB)=x+iy then ((x^2)/(sin^2A)-(y^2)/(cos^2A))+((x^2)/(cosh^2B...

    Text Solution

    |

  12. I : sum(k=1)^(6)[sin((2kpi)/(7))-icos((2kpi)/(7))]=i II : sum(r=1)...

    Text Solution

    |

  13. Match the following. {:(Column-I," "Column-II),(I" : "x=costheta...

    Text Solution

    |

  14. The ascending order of the values of z1(1+i)^4+(1-i)^4, z2=(sq...

    Text Solution

    |

  15. I : Value of i^i=e^(-pi/2) II : z=ilog(2+sqrt3) then sinz=2 wh...

    Text Solution

    |

  16. Assertion (A) : (Costheta+iSintheta)^(10)+(Costheta-iSintheta)^(10)=2c...

    Text Solution

    |

  17. The modulus argument form of 1+iTantheta when theta epsilon (pi/2,pi) ...

    Text Solution

    |

  18. If Z=(i^i)^i" where "i=sqrt(-1) then

    Text Solution

    |

  19. If alpha is a non-real and alpha=(1)^(1//5) then the value of 2^(|1+al...

    Text Solution

    |

  20. If (x-1)^4-16=0,then the sum of non-real complex values of x is

    Text Solution

    |