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If ` alpha , beta , gamma` are the roots of ` x^3 -px^2 +qx -r=0` and `r ne 0` then find `(1)/( alpha^2) +(1)/( beta^2) +(1)/( gamma ^2)` in terms of p,q ,r

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The correct Answer is:
`(q^2 -2 rp^(-))/( r^2)`
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AAKASH SERIES-THEORY OF EQUATIONS-EXERCISE -2.1 (VERY SHORT ANSWER QUESTIONS)
  1. Form the polynomial equation of degree 3 whose roots are 2,3 and 6.

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  2. find the (monic ) polynomial equation of lowest degree whose root...

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  3. Find the polynomial with rational coefficients and whose roots ...

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  4. Find the polynomial with rational coefficients and whose roots ...

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  5. Find the polynomial with rational coefficients and whose roots ...

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  6. Find the polynomial with rational coefficients and whose roots ...

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  7. Find the polynomial with rational coefficients and whose roots ...

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  8. Find the values of a,b,c,d, if 1,2,3,4 are the roots of x^4 +ax...

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  9. Find the relation between the roots and the coefficients of the cubic ...

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  10. Find the relation between the roots and the coefficients of the cubic ...

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  11. Find the roots of x^4-16x^3+86x^2-176x+105=0

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  12. If 8x^(4) - 2x^(3) - 27x^(2) + 6x + 9 = 0 then s(1), s(2), s(3) , s(4)...

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  13. If 1,-2 and 3 are roots of x^3-2x^2+ax+6=0 , then find a .

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  14. If 1,-2,3 are the roots of x^3 -6x^2 +9 x-4=0 then find ' alph...

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  15. If alpha, beta and 1 are the roots of x^3-2x^2-5x+6=0 , then find alp...

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  16. If the product of the roots of 4x^3+16x^2-9xa=0 is 9 , then find a .

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

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  18. If alpha,beta,gamma are the roots of 4x^3-6x^2+7x+3=0 then find th...

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