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The common roots of the equations z^3+2z...

The common roots of the equations `z^3+2z^2+2z+1=0` and `z^1985+z^100+1=0` are

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z1/z2|=1 and arg (z1z2)=0 , then a. z1 = z2 b. |z2|^2 = z1*z2 ...

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  2. Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h ...

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  3. The common roots of the equations z^3+2z^2+2z+1=0 and z^1985+z^100+1=0...

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  4. If z1 + z2 + z3 + z4 = 0 where bi in R such that the sum of no two ...

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  5. If the inequality (m x^2+3x+4)//(x^2+2x+2)<5 is satisfied for all x i...

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  6. If |(z-2)//(z-3)|=2 represents a circle, then find its radius.

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  7. If z1 is a root of the equation a0z^n+a1z^(n-1)+........+ (a(n-1)) z ...

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  8. If f(x)=(a1x+b1)^2+(a2x+b2)^2+...+(an x+bn)^2 , then prove that (a1b1+...

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  9. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

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  10. If |2z-1|=|z-2|a n dz1, z2, z3 are complex numbers such that |z1-alph...

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  11. If (cgt 0) and 2ax^2+3bx+5c=0 does not have any real roots, then prove...

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  12. Find the number of complex numbers which satisfies both the equations ...

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  13. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

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  14. If a x^2+b x+6=0 does not have distinct real roots, then find the leas...

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  15. |z-2-3i|^2+|z-4-3i|^2=lambda represents the equation of the circle wit...

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  16. Match the statements/expressions given in column I with the values g...

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  17. A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)...

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  18. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

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  19. Let a ,b ,c in Q^+ satisfying a > b > c . Which of the following stat...

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  20. Find the complex number satisfying system of equation z^(3)=-((omega))...

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