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If alpha , beta , gamma are the ro...

If ` alpha , beta , gamma ` are the roots of ` x^3 +px^2 +qx +r=0` then the value of `(1 + alpha^2) (1+ beta^2) (1+ gamma^2)` is

A

`(r+p)^2 +(q+1)^2`

B

`(r-p)^2 + (q-1)^2`

C

`(1+p)^2 +(1 +q)^2`

D

`(r-p)^2 +(r -q)^2`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE-II
  1. If alpha , beta , gamma are the roots of x^3 -6x -4=0 then th...

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  2. If alpha , beta , gamma are the roots of x^3 + 4x +1 =0 then th...

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  3. If alpha , beta , gamma are the roots of the equation x^3 +px...

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  4. Remove the third term from the equation x^4 +2x^3 -12 x^2 +2x -1...

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  5. Number of transformed equations of x^3 +2x^2 +x+1=0 by eliminating...

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  6. The transformed equation x^3 -5/2 x^2 -(7)/(18 ) x+(1)/( 108 )...

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  7. The transformed equation with integer co-effcients whose roots ...

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  8. If the equation whose roots are p times the roots of x^4 +2x^...

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

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  10. Assertion (A) : If 1,2,3 are the roots of ax^3 + bx ^2 +cx +d=0 ...

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  11. Assertion (A) : if x^4 -x^3 -6x^2 +4x +8=0 has a multiple root ...

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  12. Assertion (A) : If alpha , beta, gamma are the roots of x^3 -x-...

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  13. Assertion (A ) : the number of roots of x^4 +2x^3 -7x^2 -8x +12=...

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  14. Assertion (A ) : the roots x^4 -5x^2 +6=0 are +- sqrt(2) ,+-sqrt...

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  15. For k gt 0 if k sqrt(-1) is a root of the equation x^4 + 6x^...

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  16. If the roots of the equation x^3 +3px^2 + 3qx -8=0 are in a...

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  17. If the roots of the equation x^(3) - 7x^(2) + 14x - 8 = 0 are in ...

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  18. If alpha , beta , gamma are the roots of x^3 +px^2 +qx +r=0 t...

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  19. If the equation x^5 -3x^4 -5x^3 +27 x^2 - 32 x +12=0 has rep...

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  20. If alpha , beta are the roots of x^2 - 3x +a =0 and gamma ...

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