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If `a gt 1` , then the roots of the equation `(1-a)x^(2)+3ax-1=0` are

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. The real value of a for which x^2+i(a-1)x+5=0 will have a pair of con...

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  2. If a, b, c are positive then both roots of the equation ax^2 + bx+c=0

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  3. The expression a^2x^2+bx+1 will be positive for all x in R if

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  4. If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2...

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  5. The least value of ax^2+bx+c,(a>0) is

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  6. If x be real, then the maximum value of 5+4x-4x^2 will be equal to

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  7. If x^2+p x=1 is a factor of the expression a x^3+b x=c , then a^2-c^2=...

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  8. If a+b+c=0, then, the equation 3ax^(2)+2bx+c=0 has , in the interval ...

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  9. If the value of ax^2+bx+c is always an integer for integral values of ...

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  10. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

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  11. Fill in the blank : If f(x) = x+1/x , x in R Then the set of possible ...

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  12. Fill in the blank : If 1+ i is a root of the equation ix^2-3x+p = 0 wh...

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  13. Equation cos 2x+7=a(2-sin x) can have a real solution for

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  14. If alpha,beta be the roots of x^2 - x-1 = 0 and An = alpha^n +beta^n, ...

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  15. For all lambda in R, The equation ax^2+ (b - lambda)x + (a-b-lambda)= ...

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  16. Prove that (a^2 + b^2) x^2 - 2b(a+c)x + (b^2+ c^2) ge 0 for all x in R...

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  17. Let f(x)= x^4- 3x^3 + 2x^2-3x+ a.If f(sqrt-1)= 0 and a in R then prove...

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  18. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

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  19. Find all numbers p for each of which the least value of the quadratic ...

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  20. Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in ...

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