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For what values of a, does the equation ...

For what values of a, does the equation `ax^2 -(a + 1)x + 3 = 0`, have roots lying between 1 and 2.

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Find p in R for which x^2-px+p+3=0 has one root>2 and the other root<2...

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  2. For what values of a inR, the quadratic equation (a^2+1)x -(a+l)x+( a^...

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  3. For what values of a, does the equation ax^2 -(a + 1)x + 3 = 0, have r...

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  4. Find the real values of the parameter a such that (2a + 1)x^2-a(x-1) =...

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  5. Find the integral values of a for which the equation x^4-(a^2-5a+6)x^2...

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  6. Find the values of k so that the quadratic equation x^2 + 2(k-1)x + k+...

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  7. The range of real values of 'p' for which the equation 2log3^2 x-|log...

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  8. For what values of the parameter a the equation x^(4)+2ax^(3)+x^(2)+2a...

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  9. For what values of the parameter a the equation x^(4)+2ax^(3)+x^(2)+2a...

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  10. Find the integral values of a for which (a+2)x^2+2(a+1)x+a=0 will have...

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  11. Consider the inequation 9^(x) -a3^(x) - a+ 3 le 0, where a is real p...

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  12. Find t values of the parameter a such that the rots alpha,beta of the ...

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  13. If the roots of 10x^3-cx^2-54x -27 0 are in harmonic progression, then...

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  14. Find the roots alpha, beta, gamma, of x^3-11 x^2+36 x-36=0if2/beta=1/a...

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  15. If the roots of x^3+px^2+qx+r=0 are in GP find the relation between p,...

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  16. If (mr ,1//mr),r=1,2,3,4, are four pairs of values of xa n dy that sat...

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  17. If two roots of the equation x^3-px^2+qx-r=0 are equal in magnitude bu...

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  18. Solve the equation 24x^3-14x^2-63x + alpha= 0, one root being double ...

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  19. If alpha,beta,gamma be the roots of ax^3+bx^2+cx+d=0 then find the val...

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  20. If alpha,beta,gamma be the roots of ax^3+bx^2+cx+d=0 then find the val...

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