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Let alpha and beta be real numbers and z...

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

A

`beta in (-1,0)`

B

`abs(beta)=1`

C

`beta in (1,infty)`

D

`beta in (0,1)`

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The correct Answer is:
C
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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
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  3. The set {R e((2i z)/(1-z^2)): z is a complex number,|z|=1,z=+-1} is.

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  5. Find the value of 3^4

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  6. Let alpha and beta be real numbers and z be a complex number. If z^(2...

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  8. Let z be a complex number such that the imaginary part of z is nonz...

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  10. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

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  14. If z is a complex number such that |z|geq2 , then the minimum value ...

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  15. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

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  16. Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2...

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  19. If the equation z^(3)+(3+i)z^(2)-3z-(m+i)=0, " where " i=sqrt(-1) " an...

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