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If alpha, beta and gamma are the roots o...

If `alpha, beta and gamma` are the roots of `x^3 +px^2+qx+r=0` then find the following : `(beta^2+gamma^2)/(beta gamma)+(gamma^2+alpha^2)/(gamma alpha) +(alpha^2+beta^2)/(alphabeta) or sum (beta^2+gamma^2)/(beta gamma)`

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` sum (beta^2+gamma^2)/(beta gamma)=(beta^2+gamma^2)/(beta gamma)+(gamma^2+alpha^2)/(gamma alpha) +(alpha^2+beta^2)/(alphabeta)`
`=(alphabeta^2 +alphagamma^2+gamma^2beta+alpha^2beta++alpha^2gamma+beta^2gamma)/(alphabetagamma)`
`=((alphabeta+betagamma+gammaalpha)(alpha+beta+gamma)-3alphabetagamma)/(alphabetagamma)`
`=(-pq+3r)/(-r)=(pq-3r)/(r)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-THEORY OF EQUATIONS -EXERCISE -4(a)
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  2. Form polynomial equations of the lowest degree , with roots as given ...

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  3. Form polynomial equations of the lowest degree , with roots as given ...

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

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  5. if 1,1,alpha are the roots of x^3-xx^2+9x-4=0 ,then find alpha .

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  6. If -1,2 and alpha are the roots of 2x^3 +x^2-7x-6=0 , then find alp...

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

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

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  9. Find the values of s1, s2,s3 and s4 for each of the following equation...

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  10. Find the values of s1, s2,s3 and s4 for each of the following equation...

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

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  12. If alpha ,beta and gamma are the roots of x^3-2x^2+3x-4 =0 , then fi...

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

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

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

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

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

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  18. If alpha, beta,gamma are the roots of x^3-6x^2+11x-6=0 then find t...

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  19. If alpha ,beta,gamma are the roots of x^3 -7x +6=0 then find the eq...

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  20. If alpha ,beta, gamma are the roots of x^3-3ax+b=0 prove that sum ...

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