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If alphaand beta be the roots of the equ...

If `alphaand beta` be the roots of the equation `x^(2)+px+q=0`, then find the values of the quantities given below :
`alpha^(4)beta^(7)+beta^(4)alpha^(7)`

Text Solution

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The correct Answer is:
`q^(4)(3pq-q^(3));`
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CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.5
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  2. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

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  3. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

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  4. Solve by applying Sreedhar Acharya's formula - (px-1)(qx+2)+r=0

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  5. If alphaandbeta be the roots of the quadratic equation x^(2)-px+q=0, t...

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  6. If alphaandbeta be the roots of the equation 5x^(2)+7x+3=0, then find ...

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  7. If alphaandbeta be the roots of the quadratic equation x^(2)+px+q=0, t...

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  8. If alphaandbeta be the roots of the quadratic equation ax^(2)+bx+c=0, ...

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  9. If alphaandbeta be the roots of the quadratic equation px^(2)-qx+q=0, ...

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  10. If the ratio of the roots of the quadratic equation lx^(2)+nx+n=0 be p...

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  11. If one root of the equation x^(2)+(5a+2)x+5a+2=0 be 5-times of the oth...

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  12. If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be 2:...

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  13. If the sum of the roots of the equation x^2-px+q=0 be three times thei...

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  14. If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 be equ...

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  15. Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 ar...

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  16. if the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal then...

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  17. Find the condition so that the roots of the equation a/(x-a)+b/(x-b)=5...

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  18. If the roots of the equation ax^2-bx+a=0 be alpha and beta, show that ...

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  19. IF p^2/qand q^2/p are the roots of the equation 2x^2+7x-4=0, find the ...

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  20. If the ratio of the roots of the quadratic equation ax^(2)+bx+c=0 be m...

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