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The equation alpha x^(3)-2(alpha+1) x^(2...

The equation `alpha x^(3)-2(alpha+1) x^(2)+4 alpha x=0` has real roots and `alpha` is any positive integer, then the sum of the roots of the equation is

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CENGAGE-Quadratic Equations, Inequalities, Modulus and Logarithms-Question Bank
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  3. If f(x)=((x+3)^(201)(x-1)^(102)(x-5)^(305))/(x^(5)(3 x+4)^(503)), th...

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  5. Number of integral values of b for which inequality (a^(2)+1) x^(2)...

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  6. Let f(x)=ax^(2)+bx+c, a ne 0, a, b, c in I. Suppose that f(1)=0, 50 lt...

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  7. If alpha, beta be the roots of x^(2)+x+2=0 and gamma, delta be the roo...

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  8. The number of integral value(s) of a so that the graph of y=16 x^(2)+8...

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  9. Number of integral values of a such that the quadratic equation x^(2)+...

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  10. If P(x)=x^(2)+a x+1. If P(x) is a negative integer for only one real x...

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  11. If A=((log (2) 3)^(3)-(log (2) 6)^(3)-(log (2) 12)^(3)+(log (2) 24)^(3...

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  12. If a, b and c be the roots of 3 x^(3)+8 x+7=0, then the value of (a+b)...

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  13. If alpha, beta, gamma are roots of equation x^(3)-2 x^(2)-1=0 and ...

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  14. The minimum value of the expression x^(2)-k x+alpha is 6 which is obta...

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  15. If alpha, beta are the roots of the equation x^(2)-3 x-15=0, and ...

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  16. If a,b,c,d in R-{0} , such that a,b are the roots of equation x^(2)+cx...

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  17. If x+y+z=5 and x y+y z+z x=3, then the greatest value of (x) is

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  18. Number of values of x satisfying the pair of quadratic equations x^(2)...

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  19. If (y^(2)-5 y)(x^(2)+2 x+4) lt 2, for all x in R, then number of integ...

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  20. Number of integral value(s) of ' x ' satisfying the equation |2 x+1|...

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