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If the roots of the quadratic equation `(b-c)x^(2)+(c-a)x+(a-b)=0` are real and equal then prove that 2b=a+c.

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CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.5
  1. If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are r...

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  2. If the roots of the quadratic equation x^(2)-m(2x-5)-6=0 are equal, th...

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  3. The roots of the equation x^(2)+x-6=0 are

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  4. If the roots of the equation 4x^(2)-5x+2=0" are "(alpha^(2))/(beta)and...

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  5. If the product of the roots of the quadratic equation x^(2)-5kx+3e^(lo...

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  6. The quadratic equation one root of which is (2-sqrt3),"is "x^(2)-4x+1=...

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  7. If the roote of the quadratic equation x^(2)-p(x-3)-5=0 are equal then...

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  8. The product of the roots of the quadratic equation ax^(2)+cx+b=0 is .

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  9. The sum of the roots of the quadratic equation (2-sqrt3)x^(2)+x+1=0 is...

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  10. Find the quadartic equation whose one root is (3-sqrt2)

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  11. Find m, given that the difference of the roots of the equation 2x^2-12...

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  12. Find the quadartic equation whose sum of the roots is 2 and sum of the...

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  13. For what values of a, the roots of the quadratic equation x^(2)-(3a-1)...

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  14. Determine the nature of the roots of the qaudratic equation 3sqrt2x^(2...

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  15. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

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  16. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

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  17. If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0, then...

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  18. If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0, then...

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  19. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

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  20. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

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  21. Solve by applying Sreedhar Acharya's formula - (px-1)(qx+2)+r=0

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