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Let lambda in R . If the origin and the...

Let `lambda in R` . If the origin and the non-real roots of `2z^2+2z+lambda=0` form the three vertices of an equilateral triangle in the Argand lane, then `lambda` is `1` b. `2/3` c. `2` d. `-1`

A

1

B

2

C

`-1`

D

none of these

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The correct Answer is:
d
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
  1. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

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  2. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

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  3. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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  4. If z(1),z(2),z(3), represent vertices of an equilateral triangle such ...

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  5. If P,P^(') represent the complex number z(1) and its additive inverse ...

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  6. Let A(z(1)),B(z(2)),C(z(3)) be the vertices of an equilateral triangle...

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  7. The area of the triangle (in square units) whose vertices are i, omega...

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  8. Show that the complex number z, satisfying the condition arg ((z -1)/(...

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  9. If A,B,C are three points in the Argand plane representing the complex...

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  10. If z(bar(z+alpha))+barz(z+alpha)=0, where alpha is a complex constant,...

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  11. Let A,B,C be three collinear points which are such that AB.AC=1 and th...

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  12. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

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  13. If z be a complex number, then |z-3-4i|^(2)+|z+4+2i|^(2)=k represent...

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  14. In Argand diagram, O, P, Q represent the origin, z and z+ iz respectiv...

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  15. If (2z(1))/(3z(2)) is purely imaginary number, then |(z(1)-z(2))/(z(1)...

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  16. If omega is a cube root of unity then find the value of sin((omega^(10...

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  17. If center of a regular hexagon is at the origin and one of the vertice...

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  18. if the roots of the equation z^(2) + ( p +iq) z + r + is =0 are real ...

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  19. Q. Let z1, z2, z3 be three vertices of an equilateral triangle circums...

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  20. If omega is the complex cube root of unity, then the value of omega+om...

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