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IF `alpha,beta` be the roots of the equation `x^2+2px+2q^2=0` where p,q are rational `p^2+q^2` is not a perfect square, form the quadratic equation whose one root is `alpha+beta+sqrt(alpha^2+beta^2)`.

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The correct Answer is:
`x^2+4px-4q^2=0`
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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. IF alpha,beta be the roots of the quadratic equation x^2-px+q=0, find ...

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

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  3. IF alpha,beta be the roots of the equation x^2+2px+2q^2=0 where p,q ar...

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  4. IF alpha,beta be the roots of the equation cx^2+2bx+2c=0 where b,c ar...

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  5. Express the roots of the equation q^2x^2-(p^2-2q)x+1=0 in terms of tho...

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  6. If the roots of the quadratics x^2+2px+q=0 and x^2+2qx+p=0(pneq) diffe...

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  7. If one root of the equation ax^2+bx+c=0 is the square of the other, pr...

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  8. If one root of the equation ax^2+bx+c=0 is the cube of the other, prov...

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  9. If the roots of the equation ax^2+bx+c=0 are two consecutive integers ...

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  10. IF alpha and beta be the roots of ax^2+2bx+c=0 and alpha+delta,beta+de...

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  11. If the ratio of the roots of the equation x^2-2px+q^2=0 be equal to th...

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  12. IF alpha and beta be the roots of the equation x^2+px+q=0 show that al...

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  13. IF p^3-q(3p-1)+q^2=0 , find the relation between the roots of the equa...

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  14. Let a,b,c be real numbers with ane0 and let alpha,beta be the roots of...

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  15. IF alpha be a root of the quadratic equation 4x^2+2x-1=0, Let prove th...

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  16. Letalpha,beta be the roots of the equation x^2-3x+a=0 and gamma,delta ...

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  17. IF a,b,c are real, show that the roots of each of the following equati...

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  18. IF a,b,c are real, show that the roots of each of the following equati...

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  19. IF a,b, are real, show that the roots of each of the following equatio...

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  20. IF a,b,c are real, show that the roots of each of the following equati...

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