questionrEarly access

Quadratic Equations and Inequalities

Showing 50 of 157 · 157 total
  1. 1.Let x 2lim( (x-2))(rx^2+(p-2)x-2p)(x-2)^2=5 for some r,p R.
  2. 2.If the quadratic equation ( +2)x^2-3 x+4 =0, -2, has two positive roots, then the number o…
  3. 3.If the set of all solutions of |x^2+x-9|=|x|+|x^2-9| is [ , ] [ ,), then ( ^2+ ^2+ ^2 ) is…
  4. 4.Let , be the roots of the equation x^2-3x+r=0, and ( )/(2),2 be the roots of the equation …
  5. 5.Let , +2, Z, be the roots of the quadratic equation x(x+2)+(x+1)(x+3)+(x+2)(x+4)+ .+(x+n-1…
  6. 6.If , , where < , are the roots of the equation x^2-( +3)x+3=0 such that (1)/( )-(1)/( )=(1…
  7. 7.Let S=x^3+ax^2+bx+c:a,b,c N and a,b,c 20 be a set of polynomials.
  8. 8.The smallest positive integral value of a, for which all the roots of x^4-a x^2+9=0 are re…
  9. 9.The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is
  10. 10.If the domain of the function f(x)= _(10x^2-17x+7)(18x^2-11x+1) is (-,a) (b,c) (d,)-e, the…
  11. 11.If and ( < ) are the roots of the equation (-2+√3)(|x-3|)+(x-6x)+(9-2√3)=0,x 0, then ( )/(…
  12. 12.A building construction work can be completed by two masons A and B together in 22.5 days.
  13. 13.Let , be the roots of the quadratic equation 12x^2-20x+3 =0, Z.
  14. 14.The number of distinct real solutions of the equation x|x+4|+3|x+2|+10=0 is
  15. 15.Let and be the roots of the equation x^2+2ax+(3a+10)=0 such that <1< .
  16. 16.The sum of all the roots of the equation (x-1)^2-5|x-1|+6=0, is :
  17. 17.The number of real roots of the equation x |x - 2| + 3|x - 3| + 1 = 0 is :
  18. 18.Let the set of all values of p R, for which both the roots of the equation x^2-(p+2)x+(2p+…
  19. 19.Consider the equation x^2+4 x-n=0, where n [20,100] is a natural number.
  20. 20.Let the equation x(x+2)(12-k)=2 have equal roots.
  21. 21.Let and be the roots of x^2+√3x-16=0, and and be the roots of x^2+3x-1=0.
  22. 22.Let P_n= ^n+ ^n,n N.
  23. 23.If the set of all a R, for which the equation 2x^2+(a-5)x+15=3a has no real root, is the i…
  24. 24.The number of solutions of the equation ((9)/(x)-9x+2)((2)/(x)-7x+3)=0 is :
  25. 25.Let f:R-0 (-,1) be a polynomial of degree 2 , satisfying f(x)f((1)/(x))=f(x)+f((1)/(x)).
  26. 26.The sum, of the squares of all the roots of the equation x^2+|2 x-3|-4=0, is
  27. 27.The product of all the rational roots of the equation (x^2-9x+11)^2-(x-4)(x-5)=3, is equal…
  28. 28.Let _ and _ be the distinct roots of 2x^2+( )x-1=0, (0,2 ).
  29. 29.Let , ; > , be the roots of the equation x^2-√2x-√3=0.
  30. 30.Let , be the roots of the equation x^2+2√2x-1=0.
  31. 31.The sum of all the solutions of the equation [(8)^2 x-16 (8)^x+48=0] is :
  32. 32.Let , be the distinct roots of the equation x^2-(t^2-5t+6)x+1=0,t R and a_n= ^n+ ^n.
  33. 33.If 2 and 6 are the roots of the equation a x^2+b x+1=0, then the quadratic equation, whose…
  34. 34.Let and be the roots of the equation px^2+qx-r=0, where p 0.
  35. 35.Let S=x R:(√3+√2)^x+(√3-√2)^x=10.
  36. 36.Let S be the set of positive integral values of a for which ax^2+2(a+1)x+9a+4x^2-8x+32<0, …
  37. 37.If , are the roots of the equation, x^2-x-1=0 and S_n=2023 ^n+2024 ^n, then :
  38. 38.The number of real roots of the equation x|x|-5|x+2|+6=0, is :
  39. 39.Let , be the roots of the equation x^2-√2x+2=0.
  40. 40.The set of all a R for which the equation x|x-1|+|x+2|+a=0 has exactly one real root, is :
  41. 41.Let , be the roots of the quadratic equation x^2+√6x+3=0.
  42. 42.Let , , be the three roots of the equation x^3+bx+c=0.
  43. 43.Let A=x R:[x+3]+[x+4] 3, B=x R:3^x( _r=1^310^r)^x-3<3^-3x, where [t] denotes greatest inte…
  44. 44.The sum of all the roots of the equation |x^2-8x+15|-2x+7=0 is :
  45. 45.The equation e^4x+8e^3x+13e^2x-8e^x+1=0,x R has :
  46. 46.The minimum value of the sum of the squares of the roots of x^2+(3-a) x+1=2 a is:
  47. 47.The number of distinct real roots of x4 - 4x + 1 = 0 is :
  48. 48.The sum of all the real roots of the equation [(e^2x - 4)(6e^2x - 5e^x + 1) = 0] is
  49. 49.The number of distinct real roots of the equation x7 - 7x - 2 = 0 is
  50. 50.The sum of the roots of the equation [x + 1 - 2 _2(3 + 2^x) + 2 _4(10 - 2^ - x) = 0], is :