Home
Class 11
MATHS
If x=1+i is a root of the equation x^3-i...

If `x=1+i` is a root of the equation `x^3-i x+1-i=0,` then the other real root is `0` b. `1` c. `-1` d. none of these

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If one root of the equation x^2+(1-3i)x-2(1+i)=0 is -1+i, then the other root is

If one root of the equation x^(2)+(1-3i)x-2(1+i)=0 is -1+i , then the other root is

The roots of the equation x^(2)-(1-2i) x-2i =0 are -

If (1-i) is a root of the equation x^(2) +ax+b=0, then the values of a and b are-

Find the roots of the equation x+(1)/(x)=3, x ne 0

The sum of the roots of the equation x^3 + 5x + 1 = 0 is

If the roots of the equation 6x^3-11x^2+6x-1 =0 are in H.P., then the roots are

Prove that the equation Z^3+i Z-1=0 has no real roots.

The roots of the quadratic equation 2x^2+3x+1 =0 are

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Th...

    Text Solution

    |

  2. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then ar...

    Text Solution

    |

  3. If x=1+i is a root of the equation x^3-i x+1-i=0, then the other real ...

    Text Solution

    |

  4. Find the modulus, argument, and the principal argument of the complex ...

    Text Solution

    |

  5. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  6. If the expression x^2+2(a+b+c)x+3(b c+ca+a b) is a perfect square, the...

    Text Solution

    |

  7. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and a...

    Text Solution

    |

  8. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  9. if z and w are two non-zero complex numbers such that absz=absw and ar...

    Text Solution

    |

  10. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x...

    Text Solution

    |

  11. If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a se...

    Text Solution

    |

  12. If one vertex of the triangle having maximum area that can be inscribe...

    Text Solution

    |

  13. The number of complex numbers z satisfying |z-3-i|=|z-9-i|a n d|z-3+3i...

    Text Solution

    |

  14. If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots an...

    Text Solution

    |

  15. Solve the equation 3^(x^2-x)+4^(x^2-x)=25.

    Text Solution

    |

  16. If t and c are two complex numbers such that |t|!=|c|,|t|=1a n dz=(a t...

    Text Solution

    |

  17. Consider the circle |z|=r in the Argand plane, which is in fact the in...

    Text Solution

    |

  18. Solve the equation 12x^4-56 x^3+89 x^2-56 x+12=0.

    Text Solution

    |

  19. If z is a complex number such that -pi//2lt=a r g zlt=pi//2, then whi...

    Text Solution

    |

  20. P is a point on the argand diagram on the circle with OP as diameter t...

    Text Solution

    |