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Using differentiation method check how m...

Using differentiation method check how many roots of the equation `x^3-x^2+x-2=0` are real?

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve (2x-3)/(x-1)+1=(9x-x^2-6)/(x-1)dot

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

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

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  4. z=x+iy and w=(1-iz)/(1+iz) and |w|=1 ,prove that z is purely real

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  5. Let ...

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

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  7. Draw the graph of y=x^(4)+2x^(2)-8x+3 Find the number of real roots ...

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

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  9. How many real solutions does the equation x^7+14x^5+16x^3+30x-560=0 h...

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  10. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

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  11. Solve sqrt(3x^2-7x-30)-sqrt(2x^2-7x-5)=x-5.

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  12. The smallest positive integer n for which ((1+i)/(1-i))^n=1 is (a)8...

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  13. Solve sqrt(3x^2-7x-30)-sqrt(2x^2-7x-5)=x-5.

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  14. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

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  15. If x= (7+4sqrt(3)), prove that x+1//x= 14

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  16. Prove that the locus of midpoint of line segment intercepted between ...

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  17. Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.

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  18. Show that: sum(r=0)^(n-1)|z1+alpha^r z2|^2=n(|z1|^2+|z2|^2),w h e r e,...

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  19. Solve sqrt(x^2+4x-21)+sqrt(x^2-x-6)=sqrt(6x^2-5x-39.)

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  20. If alpha=(z-i)/(z+i), show that, when z lies above the real axis, alph...

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