Home
Class 12
MATHS
Let alpha,beta be real and z be a comple...

Let `alpha,beta` be real and z be a complex number. If `z^2+alphaz""+beta=""0` has two distinct roots on the line Re `z""=""1` , then it is necessary that : (1) `b"" in (0,""1)` (2) `b"" in (-1,""0)` (3) `|b|""=""1` (4) `b"" in (1,oo)`

A

`beta in (1, oo)`

B

`beta in (0, 1)`

C

`beta (-1, 0)`

D

`|beta| = 1`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos
  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE NUMERICAL ANSWER TYPE QUESTIONS|20 Videos
  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos
  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that

If z^2+alphaz+beta has one root 1-2i , then find the value of alpha-beta (alpha,beta , in R)

Let z_(1) and z_(2)q ,be two complex numbers with alpha and beta as their principal arguments suith that alpha+beta then principal arguments suiven by:

If alpha, beta are the roots of the equation x^(2)-ax+b=0 .then the equation whose roots are 2 alpha+(1)/(beta), 2 beta+(1)/(alpha) is

If alpha,beta in R are such that 1-2i (here i^(2)=-1 ) is a root of z^(2)+alpha z+beta=0 , then (alpha-beta) is equal to:

If abs(z+1)=alphaZ+beta(1+i) then z=1/2-2i then the value of abs(alpha+beta) is equal to, where alpha,betainR

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
  1. The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

    Text Solution

    |

  2. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

    Text Solution

    |

  3. Let alpha,beta be real and z be a complex number. If z^2+alphaz""+beta...

    Text Solution

    |

  4. If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...

    Text Solution

    |

  5. The area of the triangle on the Arand plane formed by the complex numb...

    Text Solution

    |

  6. If z is a complex number of unit modulus of modulus and argument thet...

    Text Solution

    |

  7. if (5z2)/(7z1) is purely imaginary number then |(2z1+3z2)/(2z1-3z2) |...

    Text Solution

    |

  8. Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...

    Text Solution

    |

  9. If a complex number z satisfies z + sqrt(2) |z + 1| + i=0, then |z| is...

    Text Solution

    |

  10. If z is a complex number such that |z|>=2 then the minimum value of |z...

    Text Solution

    |

  11. Let w(Im w != 0) be a complex number. Then the set of all complex num...

    Text Solution

    |

  12. If z(1),z(2) and z(3),z(4) are two pairs of conjugate complex numbers ...

    Text Solution

    |

  13. Let z!=i be any complex number such that (z-i)/(z+i) is a purely imagi...

    Text Solution

    |

  14. For all complex numbers z of the form 1 + ialpha, alpha in "R if z"^(2...

    Text Solution

    |

  15. A complex number z is said to be uni-modular if |z|=1. Suppose z(1) a...

    Text Solution

    |

  16. The largest value of r for which the region represented by the set {om...

    Text Solution

    |

  17. If Z is a non-real complex number, then find the minimum value of (Imz...

    Text Solution

    |

  18. A value of for which (2+3isintheta)/(1-2isintheta) purely imaginary, ...

    Text Solution

    |

  19. The point represented by 2+i in the Argand plane moves 1 unit eastward...

    Text Solution

    |

  20. Let z=1+ai be a complex number, a > 0,such that z^3 is a real number....

    Text Solution

    |