Home
Class 11
MATHS
If the six roots of x^6 = -64 are writt...

If the six roots of `x^6 = -64` are written in the form `a + ib`, where a and b are real, then the product ofthose roots for which `a > 0` 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

If the six roots of x^6 = -64 are written in the form a + ib , where a and b are real, then the product of those roots for which a lt 0 is

If the roots of x^3 -14x^2 + 56x-64 =0 are in G.P then the middle root is

If 2 + isqrt3 is a root of x^(3) - 6x^(2) + px + q = 0 (where p and q are real) then p + q is

the roots of the equation x^4 -6x^3 + 18x^2- 30 x +25 =0 are of the form a +- i b and b +- ia then (a ,b)=

If the roots of the equation x^4 - 10x^3 +50 x^2 - 130 x + 169 = 0 are of the form a +- ib and b +- ia then (a,b)=

Find the square roots of the numbers by expressing each number as the product of primes : 64

Let alpha ne 1 be a real root of the equation x^(3) - ax^(2) + ax - 1 = 0, where a ne - 1 is a real number, then a root of this equation, among the following , is :

If the roots of the equation, x^3 + px^2+qx-1 = 0 form an increasing G.P. where p and q are real,then (a) p +q = 0 (b) p in (-3, oo) (c) one of the roots is unity (d) one root is smaller than 1 and one root is greater than 1

In copying a quadratic equation of the form x^2 + px + q = 0 , the coefficient of x was wrongly written as -10 in place of -11 and the roots were found to be 4 and 6 . find the roots of the correct equation.

If a,b are real, then the roots of the quadratic equation (a-b)x^(2)-5 (a+b) x-2(a-b) =0 are

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Given alpha,beta, respectively, the fifth and the fourth non-real root...

    Text Solution

    |

  2. Solve the equation (x-1)^4+(x-5)^4=82.

    Text Solution

    |

  3. If the six roots of x^6 = -64 are written in the form a + ib, where ...

    Text Solution

    |

  4. The maximum area of the triangle formed by the complex coordinates z,...

    Text Solution

    |

  5. Solve sqrt(x+5)+sqrt(x+21)=sqrt(6x+40.)

    Text Solution

    |

  6. If zr : r=1,2,3, ,50 are the roots of the equation sum(r=0)^(50)z^r=0 ...

    Text Solution

    |

  7. The complex number associated with the vertices A, B, C of DeltaABC...

    Text Solution

    |

  8. Evaluate x=sqrt(6+sqrt(6+sqrt(6+oodot)))

    Text Solution

    |

  9. If a complex number z satisfies |2z+10+10 i|lt=5sqrt(3)-5, then the le...

    Text Solution

    |

  10. If 1,alpha1,alpha2, ,alpha(n-1) are the n t h roots of unity, prove t...

    Text Solution

    |

  11. If n >1 , show that the roots of the equation z^n=(z+1)^n are collinea...

    Text Solution

    |

  12. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

    Text Solution

    |

  13. If |z2+i z1|=|z1|+|z2| and|z1|=3 and |z2|=4, then the area of triangl...

    Text Solution

    |

  14. What is the locus of w if w=3/za n d|z-1|=1?

    Text Solution

    |

  15. If z is complex number, then the locus of z satisfying the condition...

    Text Solution

    |

  16. Find the remainder when x^3+4x^2-7x+6 is divided by x-1.

    Text Solution

    |

  17. What is the locus of z if ||z-cos^(-1)cos12|-|z-sin^(-1)s in 12||=8(pi...

    Text Solution

    |

  18. Use the factor theorem to find the value of k for which (a+2b),w h e ...

    Text Solution

    |

  19. If z is a complex number lying in the fourth quadrant of Argand plane ...

    Text Solution

    |

  20. If z=(lambda+3)+isqrt(5-lambda^2) then the locus of Z is

    Text Solution

    |