Home
Class 11
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

A

`betain(-1,0)`

B

`absbeta=1`

C

`betain[1,infty)`

D

`betain(0,1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

If z be a complex number satisfying z^4+z^3+2z^2+z+1=0 then absz is equal to

If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta are the imaginary cube roots ofunity, then xyz=

Let z_1 and z_2 , be two complex numbers with alpha and beta as their principal arguments such that alpha+beta gt pi then principal arg(z_1z_2) is given by:

If alpha is a complex constant such that alphaz^2+z+baralpha=0 has areal root then

Let z be a complex number such that the imaginary part of z is non zero and a=z^2+z+1 is real then a cannot take the value

The three angular points of a triangle are given by Z=alpha, Z=beta,Z=gamma,w h e r ealpha,beta,gamma are complex numbers, then prove that the perpendicular from the angular point Z=alpha to the opposite side is given by the equation R e((Z-alpha)/(beta-gamma))=0

Let z be a complex number satisfying |z+16|=4|z+1| . Then

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(Re z ne2) be a complex number such that z^2-4z=absz^2+16/absz^3 then the value of absz^4 is

If z_(1) and z_(2) are two complex numbers, then which of the following is true ?

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. If a, b and c are positive numbers in a G.P., then the roots of the qu...

    Text Solution

    |

  2. If the equation x^2+2x+3=0 and ax^2+bx+c=0 , a, b, c in R, have a comm...

    Text Solution

    |

  3. If alpha and beta are the roots of x^2-x+1=0,then the value of alpha^(...

    Text Solution

    |

  4. If alpha,beta are the roots of the quadratic equation x^2+ax+b=0, (bne...

    Text Solution

    |

  5. Let p(x) be a quadratic polynomial with constant term 1. Suppose p(x) ...

    Text Solution

    |

  6. If alpha,beta are the roots of the quadratic equation ax^2+bx+c=0 and ...

    Text Solution

    |

  7. Let sinalpha,cosalpha, be the roots of the equation x^2-bx+c=0. Then w...

    Text Solution

    |

  8. What is the calorific value of 80 gms of carbohydrate, 15 gms of prote...

    Text Solution

    |

  9. The equation e^(sin x) -e^(-sin x)-4=0 has

    Text Solution

    |

  10. The equations x^2+x+a=0 and x^2+ax+1=0 have a common real root

    Text Solution

    |

  11. If (alpha+sqrtbeta) and (alpha-sqrtbeta) are the roots of the equation...

    Text Solution

    |

  12. If a, b, c are in arithmetic progression, then the roots of the equati...

    Text Solution

    |

  13. The quadratic equation 2x^2-(a^3+8a-1)x+a^2-4a=0 possesses roots of op...

    Text Solution

    |

  14. A value of b for which the equations x^2+bx-1=0, x^2+x+b =0 have one r...

    Text Solution

    |

  15. Let alpha and beta be the roots of the equation x^2-6x-2=0. If an=alph...

    Text Solution

    |

  16. Let alpha,beta be real and z be a complex number. Ifz^2+alphaz+beta=0 ...

    Text Solution

    |

  17. If sintheta and costheta are the roots of the equation ax^2-bx+c=0, th...

    Text Solution

    |

  18. Let a, b, c be three number such that a+2b+4c=0. Then the equation ax^...

    Text Solution

    |

  19. If the ratio of the roots of the equation px^2+qx+r is a:b, then ab/(...

    Text Solution

    |

  20. If alpha and beta are the roots of the equation x^2+x+1=0, then the eq...

    Text Solution

    |