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If x is real, prove that the value of the expression `((x-1)(x+3))/((x-2)(x+4))` cannot be between `(4)/(9) and 1.`

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ICSE-QUADRATIC EQUATIONS-CHAPTER TEST
  1. If x is real, prove that the value of the expression ((x-1)(x+3))/((x-...

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  2. Solve the equation: 5^(x+1)+5^(2-x)=5^(3)+1

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  3. Solve the equations: sqrt((x)/(1-x))+sqrt((1-x)/(x))=(13)/(6).

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  4. Solve the equations: (x+1)(x+2)(x+3)(x+4)=120

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  5. Prove that both the roots of the equation x^(2)-x-3=0 are irrational.

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  6. For what values of m will the equation x^(2)-2mx+7m-12=0 have (i) equa...

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  7. If one root of 2x^(2)-5x+k=0 be double the other, find the value of k.

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  8. If alpha,beta be the roots of the equation x^(2)-x-1=0, determine the ...

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  9. If the roots of the equation ax^(2)+bx+c=0 be in the ratio 3:4, show t...

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  10. If x is real, prove that the quadratic expression (i) (x-2)(x+3)+7 is ...

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  11. Draw the graph of the quadratic function x^(2)-4x+3 and hence find the...

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  12. For what real values of a, will the expression x^(2)-ax+1-2a^(2), for ...

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  13. If x be real, prove that the value of (2x^(2)-2x+4)/(x^(2)-4x+3) canno...

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  14. If the roots of the equation qx^(2)+2px+2q=0 are real and unequal, pro...

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  15. If alpha,beta be the roots of x^(2)-px+q=0, find the value of alpha^(5...

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  16. If the difference between the roots of the equation x^(2)+ax+1=0 is le...

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  17. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,...

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  18. alpha,beta are the roots of ax^(2)+2bx+c=0 and alpha+delta,beta+delta ...

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  19. If alpha,beta are the roots of the equation x^(2)-2x-1=0, then what is...

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  20. If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@) and...

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  21. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

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