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Find the condition in order that the equ...

Find the condition in order that the equation `ax^4+4bx^3+6cx^2+4dx+e=0`
may have a pair of equal roots .

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AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE-III
  1. Find the condition in order that the equation ax^4+4bx^3+6cx^2+4dx+e=0...

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  2. The quotient obtained when 3x^4 -x^3 +2x^2 -2x -4 is divided by ...

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  3. The value of k so that x^4 -4x^3 +5x^2 -2x +k is divisible by ...

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  4. The equation whose roots are 1,2 +- 3i is

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  5. The polynomial equation of the lowest degree having roots 1 , ...

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  6. The equation of lowest degree with rational coefficient having ...

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  7. If one root of x^3 -6x^2 +3x +10 =0 is 2 then the remaining t...

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  8. If one root of 10 x^3 -x^2 - 278 x + 165=0 is 5 then product ...

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  9. If the product of two of the roots of x^3 +kx ^2 -3x+4=0 is -1 ...

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  10. The condition for one root of x^3+ax^2+bx+c=0 is sum of the ot...

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  11. If one of the roots of 18x^3 + 81x^2 + 121 x+60=0 is equal to ...

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  12. If the roots of the equation x^3 -9x^2 + 23x-15=0 are in A.P t...

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  13. If the roots of 24x^3 - 26 x^2 + 9x -1=0 are in H.P then the ...

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  14. If alpha , beta , gamma are the roots of x^3 -3ax^2 +3 bx -c=0...

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  15. If the root of kx^3 - 18x^2 - 36 x+8=0 are in H.P then k=

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  16. If the roots of x^3 -14x^2 + 56x-64 =0 are in G.P then the mid...

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  17. If x^4 - 12x ^3 +52 x^2 - 96 x+64=0 have pairs of equal roots t...

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  18. If the roots of x^4 -2x^3 - 21x^2 + 22 x + 40 =0 are in A.P then...

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  19. If the roots of 27x^(4) - 195x^(3) + 494x^(2) - 520x + 192 = 0 are in...

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  20. The roots of x^3 - 13x^2 +39 x-27=0 are in

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  21. If x^3 -3x^2 + 4=0 has a multiple root then that multiple root i...

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