Home
Class 12
MATHS
z1a n dz2 are the roots of 3z^2+3z+b=0. ...

`z_1a n dz_2` are the roots of `3z^2+3z+b=0.` if `O(0),(z_1),(z_2)` form an equilateral triangle, then find the value of `bdot`

Text Solution

Verified by Experts

Here, `z_(1)+z_(2)=-1,z_(1)z_(2)=(b)/(3)`
Triangle OAB is equilateral. So,
`0^(2)+z_(1)^(2)+z_(2)^(2)=0xxz_(1)+0xxz_(2)+z_(1)z_(2)`
or `(z_(1)+z_(2))^(2)-2z_(1)z_(2)=z_(1)z_(2)`
or `1=3z_(1)z_(2)=3(b)/(3)`
or `b=1`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.2|9 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

z_(1)andz_(2) are the roots of 3z^(2)+3z+b=0. if O(0),(z_(1)),(z_(2)) form an equilateral triangle,then find the value of b .

Let z_(1) and z_(2) be the roots of z^(2)+az+b=0 If the origin,z_(1) and z_(2) from an equilateral triangle,then

Let z_1,z_2 be the roots of the equation z^2+az+12=0 and z_1, z_2 form an equilateral triangle with origin. Then, the value of absa is ________ .

Let z_(1),z_(2) be the roots of the equation z^(2)+az+12=0 and z_(1),z_(2) form an equilateral triangle with origin. Then the value of |a| is

If z_1 and z_2 are the roots of the equation z^2+az+12=0 and z_1 , z_2 forms an equilateral triangle with origin. Find absa

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.

If z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .

Let z_1 and z_2 be the roots of z^2+pz+q =0. Then the points represented by z_1,z_2 the origin form an equilateral triangle if p^2 =3q.

CENGAGE-COMPLEX NUMBERS-Examples
  1. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, the...

    Text Solution

    |

  2. If z=z0+A( z -( z )0), w h e r eA is a constant, then prove that loc...

    Text Solution

    |

  3. z1a n dz2 are the roots of 3z^2+3z+b=0. if O(0),(z1),(z2) form an equi...

    Text Solution

    |

  4. Let z(1),z(2) and z(3) be three complex number such that |z(1)-1|= |z...

    Text Solution

    |

  5. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

    Text Solution

    |

  6. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

    Text Solution

    |

  7. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  8. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

    Text Solution

    |

  9. A(z1),B(z2),C(z3) are the vertices of he triangle A B C (in anticlockw...

    Text Solution

    |

  10. If one of the vertices of the square circumscribing the circle |z - 1|...

    Text Solution

    |

  11. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |

  12. Complex numbers of z(1),z(2),z(3) are the vertices A, B, C respectivel...

    Text Solution

    |

  13. Let z1, z2a n dz3 represent the vertices A ,B ,a n dC of the triangle ...

    Text Solution

    |

  14. F a=cos(2pi//7)+is in(2pi//7) , then find the quadratic equation whose...

    Text Solution

    |

  15. If omega is an imaginary fifth root of unity, then find the value of l...

    Text Solution

    |

  16. If 1, alpha(1), alpha(2), alpha(3),…….,alpha(s) are ninth roots of uni...

    Text Solution

    |

  17. find the sum of squares of all roots of the equation. x^(8) - x^(7) ...

    Text Solution

    |

  18. Find roots of the equation (z + 1)^(5) = (z - 1)^(5).

    Text Solution

    |

  19. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Argand plane, then...

    Text Solution

    |

  20. Let 1, z(1),z(2),z(3),…., z(n-1) be the nth roots of unity. Then pro...

    Text Solution

    |