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-If a,b,c in R then prove that the roots...

-If `a,b,c in R` then prove that the roots of the equation `1/(x-a)+1/(x-b)+1/(x-c)=0` are always real cannot have roots if `a=b=c`

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Show that if p,q,r and s are real numbers and pr=2(q+s), then atleast ...

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  2. If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,t h e ...

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  3. -If a,b,c in R then prove that the roots of the equation 1/(x-a)+1/(x-...

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  4. If the equations ax + by = 1 and cx^2 +dy^2=1 have only one solution, ...

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  5. If a,b,c are odd integere then about that ax^2+bx+c=0, does not have r...

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  6. Show that the equation e^(sinx)-e^(-sinx)-4=0 has no real solution.

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  7. 14 For what values of p, the roots of the equation 12(p+2)x^2-12(2p-1)...

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  8. If the ratio of the roots of the equation lx^2+nx+n=0 is p:q prove tha...

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  9. If one root of equation (l-m) x^2 + lx + 1 = 0 be double of the other ...

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  10. if the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in ma...

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  11. If one root of the quadratic equation ax^(2)+bx+c=0 is equal to the ...

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  12. If a,b,c are in G.P. then the roots of the equation a x^2 + bx + c = 0...

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  13. Let a gt 0, b gt 0 then both roots of the equation ax^(2)+bx+c=0

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  14. If alpha is a root of the equation x^2+2x-1=0, then prove that 4alpha^...

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  15. If alpha, beta are the roots of the equations x^2+px+q=0 then one of t...

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  16. Let a and b be roots of x^2-3x+p=0 and let c and d be the roots of x^...

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  17. If alpha,beta are the nonzero roots of a x^2+b x+c=0a n dalpha^2,beta^...

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  18. If alpha,beta are the roots of the equation ax^2+bx+c=0 and Sn=alpha^n...

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  19. If alpha,beta be the roots of the equation lambda^2(x^2 - x) + 2lambda...

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  20. If a, b are the roots of x^2 + px + 1 = 0 and c, d are the roots of ...

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