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Find the condition that the roots of x^3...

Find the condition that the roots of `x^3+px^2+qx+r=0` are in G.P.

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The correct Answer is:
`q^3=p^3r`
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PREMIERS PUBLISHERS-THEORY OF EQUATIONS-Problems for practice (Answer the following)
  1. Find the condition that the roots of x^3+px^2+qx+r=0 are in G.P.

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  2. If alpha and beta are the roots of 2x^2-5x+3=0 form the equation who...

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  3. If alpha and beta are the roots of 2x^2-5x+3=0 form the equation who...

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  4. If alpha,beta,gamma are the roots of x^3-2x^2+3x-4=0 find the value o...

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  5. If alpha,beta,gamma are the roots of x^3-2x^2+3x-4=0 find the value o...

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  6. Solve the equation 3x^3-7x^2-7x+3=0 given that product of two of its ...

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  7. Solve : x^3-15x^2+66x+80=0 given that the roots as in AP.

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  8. Solve x^3+7x^2+14x+8=0 given that the roots are in GP.

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  9. Solve : 3x^3-x^2+x+1=0 given the roots are in HP.

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  10. Find the polynomial equation with integer coefficients with sqrt(sqr...

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  11. Solve : 2x^3-3x^2-14x+5=0 given that 2-3i is a root

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  12. Solve : x^3-x^2-4x-2=0 given that 1+sqrt3 is a root .

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  13. Solve : x^6-6x^5+10x^4-9x^2+6x-2=0 given that (2+sqrt3) and (1+i) are ...

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  14. Solve : x^6-6x^5+13x^4-12x^3+7x^2-6x-5=0 if (1+sqrt2) and (2+i) are r...

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  15. Solve 2x^3-11x^2+10x-1=0

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  16. Solve x^3-3x^2-9x-5

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  17. Solve x^4-4x^2-5=0

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  18. Solve 6x^6-35x^5+56x^4-56x^2+35x-6=0

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  19. Solve 3x^4-10x^3+10x-3=0

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  20. Show that 3x^9-10x^5+3x^4+2x^2+7=0 has at least 6 imaginary roots.

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  21. Find the least no. of imaginary roots of 2x^9+3x^5-5x^4-9x^2+2

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