Home
Class 11
MATHS
Let 1,w,w^2 be the cube root of unity. T...

Let `1,w,w^2` be the cube root of unity. The least possible degree of a polynomial with real coefficients having roots `2w ,(2+3w),(2+3w^2),(2-w-w^2)` is _____________.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

Let I, omega and omega^(2) be the cube roots of unity. The least possible degree of a polynomial, with real coefficients having 2omega^(2), 3 + 4 omega, 3 + 4 omega^(2) and 5- omega - omega^(2) as roots is -

If 1,omega,omega^2 are the cube roots of unity, then /_\ is equal to.....

If omega is a cube root of unity, then 1+omega = …..

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then omega + omega^(2)= …..

If omega is a cube root of unity, then 1+ omega^(2)= …..

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega,omega^(2) are cube roots of unity then the value of (2+2omega-3omega^(2))^(3) is

If 1, omega, omega^(2) are cube roots of unity, prove that 1, omega, omega^(2) are vertices of an equilateral triangle

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega^(2))^(4)= omega

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let |(( bar z 1)-2( bar z 2))//(2-z1( bar z 2))|=1 and |z2|!=1,where z...

    Text Solution

    |

  2. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 b...

    Text Solution

    |

  3. Let 1,w,w^2 be the cube root of unity. The least possible degree of a ...

    Text Solution

    |

  4. If z1a n dz2 are complex numbers and u=sqrt(z1z2) , then prove that |z...

    Text Solution

    |

  5. The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a...

    Text Solution

    |

  6. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  7. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

    Text Solution

    |

  8. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is

    Text Solution

    |

  9. Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z ...

    Text Solution

    |

  10. (costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

    Text Solution

    |

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

    Text Solution

    |

  12. Identify locus z if R e(z+1)=|z-1|

    Text Solution

    |

  13. If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of...

    Text Solution

    |

  14. Solve the equation sqrt(a(2^x-2)+1)=1-2^x ,x in Rdot

    Text Solution

    |

  15. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the va...

    Text Solution

    |

  16. Let Z1 = (8 + i)sin theta + (7 + 4i)cos theta and Z2 = (1 + 8i)sin th...

    Text Solution

    |

  17. For a<0, determine all real roots of the equation x^2-2a|x-a|-3a^2=0.

    Text Solution

    |

  18. Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at ...

    Text Solution

    |

  19. Express the following in a+i b form: ((cosalpha+isinalpha)^4)/((sinbe...

    Text Solution

    |

  20. Find the root of equation 2x^2+10 x + 20=0.

    Text Solution

    |