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If the roots alpha and beta of the quadr...

If the roots `alpha` and `beta` of the quadratic equation `ax^2+bx+c`=0 are real and of opposite sign.then show that roots of the equation `alpha(x-beta)^2+beta(x-alpha)^2`=0 are also real and of opposite sign.

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. Let alpha and beta be the roots of the equation ax^2+2bx+c=0 and alpha...

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  2. If sin theta,costheta are the roots of the equation ax^2+bx+c=0 then f...

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  3. If the roots alpha and beta of the quadratic equation ax^2+bx+c=0 are ...

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  4. If x^2-px+4gt0 for all real 'x' then find 'p'

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  5. For xinR, Prove that the given expression (x^2+34x-71)/(x^2+2x-7) can ...

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  6. If a,b,cinR : ane0 and the quadratic equation ax^2+bx+c=0 has no real ...

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  7. Find the values of the parameter a for which the roots of the quadrati...

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  8. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  9. Find the value of a which the equation 4x^2-2x+a=0 has two roots lying...

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  10. Find the set of all x for which : (2x)/(2x^2+5x+2)gt1/(x+1)

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  11. Solve the following inequalities : (x-1)/(x^2-4x+3)lt1

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  12. Solve the following inequalities : (x^2-2x-1)/(x+1)ltx

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  13. Solve the following inequalities : (x-1)/(x)-(x+1)/(x-1)lt2

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  14. Solve the equation (x^2-6x)^2=81+2(x-3)^2

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  15. Solve log(1/3)(x^2-3x+5)lt-1

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  16. If alpha,beta,gamma are the roots of x^3+ax+b=0, then the value of alp...

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  17. Find the number of redered pairs (x,y) satisfying x^2+1=y and y^2+1=x

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  18. The roots of the quadratic equation 2x^2+3x+1=0 are

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  19. The number of values of 'a' for which (a^2-3a+2)x^2+(a^2-5a+6)x+a^2-4...

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  20. If a and b are integers and 2-sqrt3 is a root of the equation 3x^2+ax+...

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