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If one root of the equation ax^2+bx+c=0 ...

If one root of the equation `ax^2+bx+c=0` is the square of the other, prove that , `b^3+ac^2+a^2c=3abc`.

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If one root of the equation ax^2+bx+c=0 is square the other root, then prove that b^3+ac^2+a^2c= 3abc .

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Long Answer type question)
  1. Express the roots of the equation q^2x^2-(p^2-2q)x+1=0 in terms of tho...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show...

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  18. Find the condition that the roots of the quadratic equation x^2+px+q=0...

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  19. Find the condition that the roots of the quadratic equation x^2+px+q=0...

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  20. Find the condition that the roots of the quadratic equation x^2+px+q=0...

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