Home
Class 12
MATHS
If x^2 + ax + b is an integer for every ...

If `x^2 + ax + b` is an integer for every integer x then

A

'a' is always an integer but 'b' need not be an integer.

B

'b' is always an integer but 'a' need not be an integer.

C

a + b is always an integer.

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|20 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - I|3 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|28 Videos
  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

If x^2+ax+b is an integer for every integral value of x and roots of equation x^2+ax+b=0 are rational then is (A) both roots are integers (B) one is an integer and the othe is not (C) no root is an integer (D) one root is zero and other is non zero

If p is an integers, then every square integer is of the form

For some integer q , every odd integer is of the form

For some integer m , every even integer is of the form

Let f(x)=Ax^(2)+Bx+c, where A,B,C are real numbers.Prove that if f(x) is an integer whenever x is an integer,then the numbers 2A,A+B, and C are all integer. Conversely,prove that if the number 2A,A+B, and C are all integers,then f(x) is an integer whenever x is integer.

For how many real values of k is 6kx^2 + 12kx -24x + 16 a perfect square for every integer x?

If the value of ax^2+bx+c is always an integer for integral values of x where a, b, c are rationals then a+b must be an integer.

Let n be a four-digit integer in which all the digits are different.If x is number of odd integers and y is number of even integers, then a.x y c.x+y=4500 d.|x-y|=54

If x is a negative integer, -x is a positive integer.

FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. If p(x)=ax^(2)+bx and q(x)=lx^(2)+mx+n with p(1)=q(1), p(2)-q(2)=1, an...

    Text Solution

    |

  2. Number of ordered pair (x, y) satisfying x^(2)+1=y and y^(2)+1=x is

    Text Solution

    |

  3. If x^2 + ax + b is an integer for every integer x then

    Text Solution

    |

  4. The solution of (x)^(2)+(x+1)^(2)=25 (where (.) denotes the least inte...

    Text Solution

    |

  5. The equation x^2 + nx + m = 0, n, m in I can not have

    Text Solution

    |

  6. f(x) is a polynomial of degree three with rational co - efficients. If...

    Text Solution

    |

  7. If alpha, beta be the roots of ax^(2)+bx+c=0(a, b, c in R), (c )/(a)lt...

    Text Solution

    |

  8. The solution of the equation 1!+2!+3!+…+x!=k^(2) where k in l are

    Text Solution

    |

  9. If the equation x^2-(2 + m)x + (m2-4m +4) = 0 has coincident roots, th...

    Text Solution

    |

  10. Let f(x)=a x^2+b x+c ,if f(-1)lt1,f(1)gt-1,f(3)lt-4 and a!=0 then

    Text Solution

    |

  11. lf p, q, r in R and the quadratic equation px^2 + qx + r = 0 has no re...

    Text Solution

    |

  12. If x^2-4x+log(1/2)a=0 does not have two distinct real roots, then maxi...

    Text Solution

    |

  13. The least value of |a| for which tan theta and cot theta are the roots...

    Text Solution

    |

  14. If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots,...

    Text Solution

    |

  15. The value of a for which exactly one root of the equation e^(a)x^(2)-e...

    Text Solution

    |

  16. If alphaa n dbeta are the roots of x^2-a(x-1)+b=0 then find the value ...

    Text Solution

    |

  17. Consider the equation x^(3)-nx+1=0, n in N, n ge 3. Then

    Text Solution

    |

  18. If sin alpha, sin beta and cos alpha are in GP, then roots of x^2 + 2x...

    Text Solution

    |

  19. If a, b in (0, 2) and the equation (2x^2+5)/2 = x - 2cos(ax + b) has a...

    Text Solution

    |

  20. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

    Text Solution

    |