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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

`|beta|=1`

B

`betain(1,oo)`

C

`betain(0,1)`

D

`betain(-1,0)`

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-COMPLEX NUMBERS -EXERCISE 1
  1. In the Argrand plane, the points represented by the complex numbers 1+...

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  2. In the Argrand plane, the points represented by the complex numbers 2-...

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  3. Are of the triangle formed by the three complex numbers, 1+i,1-i,2i in...

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  4. Area of the triangle formed by the Argrand diagram formed by the compl...

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  5. If |z|=3 , then area of the triangle whose sides are z , omegaz and z ...

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  6. If the area of the triangle on the complex plane formed the points z ,...

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  7. If a and b are real number between 0 and 1 such that the points z1=a+I...

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

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  9. If z1,z2,z3 are the vertices of a triangle then its centroid is

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  10. Let the complex number z1,z2,z3 be the vertices of an equilateral tria...

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  11. ABC is an isosceles triangle and B=90 . If B and the midpoint P of AC...

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  12. If three complex number are in A.P then they lie on

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  13. If the Argand plane, the points represented by the complex numbers 7-4...

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  14. In the Argand plane, the points represented by the complex numbers 2-6...

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  15. The condition for the points z1,z2,z3,z4 taken in order in the Argand ...

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  16. The straight line joining the points in Argrand diagram given by 0+0i ...

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  17. The equation of the line joining the points represented by 2 - 3i and ...

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  18. The equation of the perpendicular bisector of the line joining the poi...

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  19. If a is a complex number and b is a real number then the equation bar...

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

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