Home
Class 12
MATHS
Let f(x)=x^(2)+ax+b be a quadratic polyn...

Let `f(x)=x^(2)+ax+b` be a quadratic polynomial in which a and b are integers. If for a given integer `n, f(n) f(n+1)=f(m)` for some integer m, then the value of m is

A

`n(a+b)+ab`

B

`n^(2)+an+b`

C

`n(n+1)+an+b`

D

`n^(2)n+a+b`

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

For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=

Let f(x) be a quadratic polynomial with integer coefficients such that f(0) and f(1) are odd integers.then prove that the equation f(x)=0 does not have an integer solution

Let f:N to N for which f(m+n)=f(m)+f(n) forall m,n in N .If f(6)=18 then the value of f(2)*f(3) is

Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x) takes the value p, a prime for two distinct integer values of x, then the number of integer values of x for which f (x) takes the value 2p is :

If I,n are positive integers, 0 < f < 1 and if (7+4sqrt3)^n=I+f , then the value of (I+f)(1-f)=

Let f(x)=x^((m)/(n)) for x in R where m and n are integers,m even and n odd and '0

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

Let f(x)=ax^(2)+bx+c, where a,b,care integers.Suppose f(1)=0,40

Let f be a function from the set of all non-negative integers into itself such that f(n + 1) = 6f(n) + 1 and f(0) = 1 , then the value of f(4) – f(3)

FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. Let f(x)=x^2+b x+c ,w h e r eb ,c in Rdot If f(x) is a factor of both...

    Text Solution

    |

  2. The number of real solution of the equation (9/10)^x = -3+x-x^2 is

    Text Solution

    |

  3. Let f(x)=x^(2)+ax+b be a quadratic polynomial in which a and b are int...

    Text Solution

    |

  4. The square of sum of the roots of the equation x^(3)+2x^(2)+2x+1=0 equ...

    Text Solution

    |

  5. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |