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If alpha, beta, gamma are the roots of x...

If `alpha, beta, gamma` are the roots of `x^(3) + 2x^(2) - 4x - 3 = 0` then the equation whose roots are `alpha//3, beta//3, gamma//3` is

A

`3x^(3) + 5x^(2) - 7x - 1 = 0 `

B

`9x^(3) + 6x^(2) - 4x - 1= `0

C

`x^(3) - 3x^(2) + 8x^(2) + 4 = 0`

D

`10x^(3) - 13x^(2) + 18x^(2) + 40` = 0

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If alpha , beta , gamma are the roots of x^3 + 3x^2 -4x +2=0 then the equation whose roots are (1)/( alpha beta) ,(1)/( beta gamma) ,(1)/( gamma alpha) is

DIPTI PUBLICATION ( AP EAMET)-THEORY OF EQUATIONS-EXERCISE 1B
  1. The cubic equation whose roots are thrice to each of the roots of x^(3...

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  2. Find the algebraic equation whose roots are 2 times the roots of x^5...

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  3. If alpha, beta, gamma are the roots of x^(3) + 2x^(2) - 4x - 3 = 0 the...

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  4. If 2, - 2, 4 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the ...

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  5. If 1, -2, 3 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the roo...

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  6. If the roots of ax^(3) + bx^(2) +cx + d = 0 are in G.P. then the root...

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  7. The equation whose roots are reciprocals of the roots of 6x^(6) - 25x^...

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  8. Let alpha ne 1 be a real root of the equation x^(3) - ax^(2) + ax - 1 ...

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  9. If 3/4, -5/2, 1/2 , -3 are the roots of ax^(4) + bx^(3) + cx^(2) + dx ...

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  10. If the roots of ax^(3) + bx^(2) + cx +d = 0 are in A.P then the roots ...

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  11. If the roots of ax^(3) + bx^(2) + cx +d = 0 are in H.P then the roots ...

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  12. If the roots of ax^(3) + bx^(2) + cx +d = 0 are in G.P then the roots ...

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  13. The equation whose roots are exceed by 1 then those of x^(3) - 5x^(2) ...

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  14. The equation whose roots are exceed by 2 then those x^(4) + x^(3) - 10...

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  15. The equation whose roots are exceed by 1 then those of x^(5) + 5x^(4) ...

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  16. The equation whose roots are diminish by 1 than those of x^(3) + 2x^(2...

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  17. The equation whose roots are diminish by 3 then those of x^(4) - 5x^(3...

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  18. The equation whose roots are diminish by 3 then those x^(5) - 4x^(4) +...

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  19. If 2, -3 , 5 are the roots of ax^(3) + bx^(2) + cx + d = 0 then the ro...

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  20. If pm 2, pm 3 are the roots of ax^(4) + bx^(3) + cx^(2) + dx + e = 0...

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