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Find the condition if the roots of `a x^2+2b x+c=0 and b x^2-2sqrt(a c )x+b=0` are simultaneously real.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

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  3. Find the condition if the roots of a x^2+2b x+c=0 and b x^2-2sqrt(a c ...

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  4. Locus of complex number satisfying "a r g"[(z-5+4i)/(z+3-2i)]=pi/4 is ...

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  5. Solve (x^2-5x+7)^2-(x-2)(x-3)=1.

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  6. If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has...

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  7. Solve the equation x^4-5x^2+4=0.

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  8. The complex number z satisfies z+|z|=2+8i. find the value of |z|-8

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  9. Solve (x^2-2x-3)/(x+1)=0.

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  10. If omega is a cube root of unity and (1+omega)^7=A+Bomega then find th...

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  11. Solve (x^3-4x)sqrt(x^2-1)=0.

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  12. The complex number sinx+icos2x and cosx-isin2x are conjugate to each o...

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  13. Solve (2x-3)/(x-1)+1=(9x-x^2-6)/(x-1)dot

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  14. The points, z1,z2,z3,z4, in the complex plane are the vertices of a pa...

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  15. Using differentiation method check how many roots of the equation x^3-...

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  16. If z=x+iy and w=(1-iz)/(z-i), then |w|=1 implies that in the complex ...

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  17. If the difference between the roots of the equation x^2+""a x""+""1...

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  18. |z-4| < |z-2| represents the region given by: (a) Re(z) > 0 (b) Re(z) ...

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  19. Find how many roots of the equations x^4+2x^2-8x+3=0.

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  20. If z=[(sqrt(3)/2)+i/2]^5+[((sqrt(3))/2)-i/2]^5 , then a. R e(z)=0 b. I...

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