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Given that roots of x^3+3px^2+3qx+r=0 ...

Given that roots of `x^3+3px^2+3qx+r=0`
(iii) H.P ,. Show that `2q^3=r(3pq-r)`

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The correct Answer is:
`rArr 2q^3=r(3pq-r) `is the required condition .
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-THEORY OF EQUATIONS -EXERCISE -4(b)
  1. Given that roots of x^3+3px^2+3qx+r=0 are in (i)A.P., show that 2p^...

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  2. Given that roots of x^3+3px^2+3qx+r=0 are in G.P. show that p^3 r=...

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  3. Given that roots of x^3+3px^2+3qx+r=0 (iii) H.P ,. Show that 2q^3=r...

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  4. Find the condition that x^3-px^2+qx-r=0 may have the roots in G.P .

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  5. Solve 9x^3-15x^2+7x-1=0 , given that two of its roots are equal .

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  6. Given that one root of 2x^3+3x^2-8x+3=0 is double of another root , f...

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  7. Solve x^3-9x^2+14x +24-0 , given that two of the roots are in the rati...

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  8. Solve the following equation ,given that the root of each are in A.P ....

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  9. Solve the following equation ,given that the root of each are in A.P ....

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  10. solve the following equations , given that the roots of each are in G....

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  11. solve the following equations , given that the roots of each are in G....

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  12. Solve the following equations , given that the roots of each are in H....

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  13. Solve the following equations , given that the roots of each are in H....

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  14. solve the following equation , given that they have multiple roots . ...

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  15. solve the following equation , given that they have multiple roots . ...

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  16. Solve x^4+x^3-16x^2-4x+48=0 that the product of the two roots is 6 .

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  17. solve 8x^4-2x^3-27x^2+6x+9=0 given that two roots have the same absolu...

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  18. Solve 18x^3+81x^2+121x+60=0 given that one roots is equal to half the ...

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  19. Find the condition in order that the equation ax^4+4bx^3+6cx^2+4dx+e=0...

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  20. Show that x^5-5x^3+5x^2-1=0 has three equal roots and find this roots...

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