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Quadratic Equations and Inequalities

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  1. 101.The sum of all the real values of x satisfying the equation 2(x-1)(x2 + 5x - 50) = 1 is :
  2. 102.If tanA and tanB are the roots of the quadratic equation, 3x2 - 10x - 25 = 0, then the val…
  3. 103.If an angle A of a [ ]ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equat…
  4. 104.Let p, q and r be real numbers (p [ ] q, r [ ] 0), such that the roots of the equation [1 …
  5. 105.If [ ] and [ ] are the roots of the quadratic equation, x2 + x sin [ ] - 2 sin [ ] = 0, [ …
  6. 106.All the pairs (x, y) that satisfy the inequality [2^ ^2x - 2 x + 5 .1 4^ ^2y 1] also satis…
  7. 107.The value of [ ] such that sum of the squares of the roots of the quadratic equation, x2 +…
  8. 108.Consider the quadratic equation (c -- 5)x2 -- 2cx + (c -- 4) = 0, c [ ] 5.
  9. 109.Let [ ] and [ ] be the roots of the quadratic equation x2 sin [ ] -- x(sin [ ] cos [ ] + 1…
  10. 110.If one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, …
  11. 111.If [ ] be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m -- 4)x + 2 = …
  12. 112.The sum of the solutions of the equation [| x - 2 | + x ( x - 4 ) + 2 = 0] (x > 0) is equa…
  13. 113.If m is chosen in the quadratic equation (m2 + 1) x2 -- 3x + (m2 + 1)2 = 0 such that the s…
  14. 114.Let p, q [ ] R.
  15. 115.The number of all possible positive integral values of [ ] for which the roots of the quad…
  16. 116.If both the roots of the quadratic equation x2 - mx + 4 = 0 are real and distinct and they…
  17. 117.Let f(x) be a quadratic polynomial such that f(--1) + f(2) = 0.
  18. 118.Let [ ] and [ ] be the roots of the equation 5x2 + 6x -- 2 = 0.
  19. 119.The set of all real values of [ ] for which the quadratic equations, ([ ]2 + 1)x2 -- 4[ ]x…
  20. 120.If [ ] and [ ] are the roots of the equation x2 + px + 2 = 0 and [1 ] and [1 ] are the roo…
  21. 121.Let [ 0] be in R.
  22. 122.Let [ ] and [ ] be the roots of x2 - 3x + p=0 and [ ] and [ ] be the roots of x2 - 6x + q …
  23. 123.Let [t] denote the greatest integer [ ] t.
  24. 124.If [ ] and [ ] are the roots of the equation, 7x2 -- 3x -- 2 = 0, then the value of [ 1 - …
  25. 125.If [ ] and [ ] be two roots of the equation x2 -- 64x + 256 = 0.
  26. 126.Let [ ] and [ ] be the roots of the equation x2 - x - 1 = 0.
  27. 127.Let [ ] and [ ] be two real roots of the equation (k + 1)tan2x - [ 2 ] .
  28. 128.Let S be the set of all real roots of the equation, 3x(3x -- 1) + 2 = |3x -- 1| + |3x -- 2…
  29. 129.Let a, b [ ] R, a [ ] 0 be such that the equation, ax2 -- 2bx + 5 = 0 has a repeated root …
  30. 130.Let [x] denote the greatest integer less than or equal to x.
  31. 131.Let p and q be two positive numbers such that p + q = 2 and p4+q4 = 272.
  32. 132.Let [] and [] be the roots of x2 - 6x - 2 = 0.
  33. 133.The integer 'k', for which the inequality x2 - 2(3k - 1)x + 8k2 - 7 > 0 is valid for every…
  34. 134.If [x] be the greatest integer less than or equal to x, then [_n = 8^100 [ ( - 1)^nn 2 ] ]…
  35. 135.The set of all values of K > -1, for which the equation [(3x^2 + 4x + 3)^2 - (k + 1)(3x^2 …
  36. 136.Let [ = _x R 8^2 3x.4^4 3x ] and [ = _x R 8^2 3x.4^4 3x ].
  37. 137.Let [], [] be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0.
  38. 138.If the sum of the squares of the reciprocals of the roots [] and [] of the equation 3x2 + …
  39. 139.If [, ] are the roots of the equation [ x^2-(5+3^ _3 5-5^ _5 3)x+3(3^( _3 5)^(1)/(3)-5^( _…
  40. 140.Let [], [] be the roots of the equation [x^2-√2 x+√6=0] and [1^2+1, 1^2+1] be the roots of…
  41. 141.Let [] be a root of the equation 1 + x2 + x4 = 0.
  42. 142.Let [S_1 = x R - 1,2 :(x + 2)(x^2 + 3x + 5) - 2 + 3x - x^2 0 ] and [S_2 = x R:3^2x - 3^x +…
  43. 143.Let S be the set of all integral values of [] for which the sum of squares of two real roo…
  44. 144.The number of integral values of k, for which one root of the equation 2x^2-8x+k=0 lies in…
  45. 145.Let [S = x:x R,and,( 3 + 2 )^x^2 - 4 + ( 3 - 2 )^x^2 - 4 = 10 ].
  46. 146.The number of real solutions of the equation [3( x^2 + 1 x^2 ) - 2( x + 1 x ) + 5 = 0], is
  47. 147.The equation [x^2 - 4x + [x] + 3 = x[x]], where [[x]] denotes the greatest integer functio…
  48. 148.Let [ 0] be a real number.
  49. 149.The equation e^4 x+8 e^3 x+13 e^2 x-8 e^x+1=0, x R has :
  50. 150.The number of real roots of the equation [x^2-4 x+3+x^2-9=√4 x^2-14 x+6], is :