Home
Class 12
MATHS
Let z(1)" and "z(2) be two roots of the ...

Let `z_(1)" and "z_(2)` be two roots of the equation `z^(2)+az+b=0`, z being complex number further, assume that the origin, `z_(1)" and "z_(2)` form an equilateral triangle, then

A

`a^(2)= 2b`

B

`a^(2)= 3b`

C

`a^(2)= 4b`

D

`a^(2)= b`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

Let z_(1)" and "z_(2) be the roots of the equation z^(2)+pz+q=0 , where p,q are real. The points represented by z_(1),z_(2) and the origin form an equilateral triangle if

Let z_(1)" and "z_(2) be two complex numbers such that z_(1)z_(2)" and "z_(1)+z_(2) are real then

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

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

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg z_(1)- arg z_(2) is equal to

Consider the equation z^(2)-2z+4=0 . (i) Find two complex numbers z_(1)" and "z_(2) satisfying the above equation. (ii) Simplify (z_1)/(z_2)+(z_2)/(z_1) .

If z_(1),z_(2)" and "z_(3) are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z_(1),z_(2)" and "z_(3) taken in order is

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg ((z_1)/(z_2)) is equal to

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If ((1+i)/(1-i))^(x)=1, then

    Text Solution

    |

  2. If z and omega are two non-zero complex numbers such that |z omega|=1"...

    Text Solution

    |

  3. Let z(1)" and "z(2) be two roots of the equation z^(2)+az+b=0, z being...

    Text Solution

    |

  4. Let two numbers have arithmetic mean 9 and geometric mean 4. Then thes...

    Text Solution

    |

  5. If (1-p) is a root of quadratic equation x^(2)+px+(1-p)=0 then its roo...

    Text Solution

    |

  6. If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(...

    Text Solution

    |

  7. Let z, omega be complex numbers such that bar(z)+ibar(omega)=0" and "a...

    Text Solution

    |

  8. If z= x-iy" and "z^(1/3)= p+iq, then (((x)/(p)+(y)/(q)))/((p^(2)+q^(2)...

    Text Solution

    |

  9. If |z^(2)-1|=|z^(2)|+1, then z lies on

    Text Solution

    |

  10. If z(1)" and "z(2) are two non-zero complex numbers such that |z(1)+z(...

    Text Solution

    |

  11. If omega=(z)/(z-(1/3)i)" and "|omega|=1, then z lies on

    Text Solution

    |

  12. If the cube roots of unity are 1, omega, omega^(2) then the roots of t...

    Text Solution

    |

  13. The value of a for which the sum of the squares of the roots of the eq...

    Text Solution

    |

  14. If the both roots of the equation x^(2)-bx+c=0 be two consecutive inte...

    Text Solution

    |

  15. If the both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 ...

    Text Solution

    |

  16. Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-1)+ . . .+a^(n-1)x+a^(...

    Text Solution

    |

  17. If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@)" an...

    Text Solution

    |

  18. All the values of m for which both roots of the equation x^(2)-2mx+m^(...

    Text Solution

    |

  19. The value of is sum(k=1)^(10)(sin"" (2k pi)/(11)+ icos ""(2k pi)/(11))...

    Text Solution

    |

  20. If z^(2)+z+1=0, where z is a complex number, then the value of (z+(1)/...

    Text Solution

    |