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If the sum of the roots of the equation `x^(2)-px+q=0` be m times their difference, prove that `p^(2)(m^(2)-1)=4m^(2)q`.

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ICSE-QUADRATIC EQUATIONS-EXERCISE 10 (c)
  1. If alpha,beta are the roots of the equation 3x^(2)-6x+4=0, find the va...

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  2. If alpha,beta are the roots of ax^(2)+bx+c=0, find the value of (i) ...

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  3. If the sum of the roots of the equation x^(2)-px+q=0 be m times their ...

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  4. If one root of the equation x^(2)+ax+8=0 is 4 while the equation x^(2)...

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  5. Find the value of a for which one root of the quadratic equation (a^(2...

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  6. If alpha,beta are the roots of the equation ax^(2)-bx+b=0, prove that ...

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  7. If alpha and beta are the roots of the equation x^(2)+x-7=0, form the ...

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  8. If alpha and beta are the roots of the equation 2x^(2)+3x+2=0, find th...

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  9. Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha), w...

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  10. If alpha and beta are the roots of the equation 2x^(2)-3x+1=0, form th...

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  11. If a ne b and a^(2)=5a-3,b^(2)=5b-3, then form that equation whose roo...

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  12. Given that alpha and beta are the roots of the equation x^(2)=x+7. (...

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  13. Given that alpha and beta are the roots of the equation x^(2)-x+7=0, f...

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  14. Given that alpha and beta are the roots of the equation 2x^(2)-3x+4=0,...

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  15. The roots of the quadratic equation x^(2)+px+8=0 are alpha and beta. ...

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  16. If the roots of x^(2)-bx+c=0 be two consecutive integers, then find th...

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  17. The roots of the equation px^(2)-2(p+1)x+3p=0 are alpha and beta. If a...

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  18. The roots of the equation ax^(2)+bx+c=0 are alpha and beta. Form the q...

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  19. Two candidates attempt to solve a quadratic equation of the form x^(2)...

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  20. Given that alpha and beta are the roots of the equation x^(2)=7x+4, ...

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