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The condition that the root of x ^(3) + ...

The condition that the root of `x ^(3) + 3px ^(3) +3qx +r =0` are in H.P. is :

A

`2p ^(3) -3pqr + r ^(2) =0`

B

`3p 6(3) -2pqr+p^(2) =0`

C

`2q ^(3) -3pqr+ r ^(2)=0`

D

`r ^(3) +3pqr+2q ^(3) =0`

Text Solution

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The correct Answer is:
C
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VK JAISWAL ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The condition that the root of x ^(3) + 3px ^(3) +3qx +r =0 are in H.P...

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  2. Let f(x) = ax^2 + bx + c where a,b,c are integers. If sin\ pi/7 * sin\...

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  3. Let a,b,c,d be distinct integers such that the equation (x-a) (x-b) (x...

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  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=0--(1), w...

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  5. The number of positive integral values of m, m le 16 for which the equ...

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  6. If the equation (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then...

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  7. The least rositive integral value of 'x' satisfying (e ^(x) -2) (sin (...

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  8. The integral values of x for which x^2 +17x+71 is perfect square of a ...

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  9. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

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  10. The number of real values of 'a' for which the largest value of the fu...

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  11. The number of all values of n, (whre pi is a whole number ) for which ...

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  12. The number of negative intergral values of m for which the expression ...

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  13. If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 w...

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  14. The smallest value of k for which both roots of the equation x^(2)-8kx...

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  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  16. The sum of all real values of k for which the expression x ^(2)+2xy +k...

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  17. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  18. Find the number of integral vaues of 'a' for which the range of functi...

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  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  20. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  21. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

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