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 PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

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

z_(1) and z_(2) are two non-zero complex numbers, they form an equilateral triangle with the origin in the complex plane. Prove that z_(1)^(2)-z_(1)z_(2)+z_(2)^(2)=0

if z_1, z_2, z_3 are the vertices pf an equilateral triangle inscribed in the circle absz=1 and z_1=i , then

If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solution, find the value of adot

If iz^3+z^2-z+i=0 then the value of abs(z) is

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If z^2+abs(z)^2=0 then find the imaginary value of z

If a rg(z_1)=170^0 and arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to a. 1 b. 3 c. 5 d. 7

If z_1,z_2,z_3 are the vertices of an equilateral triangle with z_0 as its circum centre, the changing origin to z_0 new vertices become z_1',z_2',z_3' show that z_1'^2+z_2'^2+z_3'^2=0

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  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 sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-...

    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 z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

    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)+isin(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 Arg and plane, the...

    Text Solution

    |

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

    Text Solution

    |