Home
Class 12
MATHS
Let f (x) =ax ^(2) +bx+c, where a,b,c ar...

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 :

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

The number of integer values of a for which x^2+ 3ax + 2009 = 0 has two integer roots is :

Let f(x) = ax^(2)+bx+c where a,b,c are real numbers. If the numbers 2a ,a +b and c are all integers ,then the number of integral values between 1 and 5 that f(x) can takes is______

If f(x) = px +q, where p and q are integers f (-1) = 1 and f (2) = 13, then p and q are

A function is defined as f(x)=(x^2+1)/(3x-2) . Can f(x) take a value 1 for any real x ? Also find the value (s) of x for which f(x) takes the value 2.

If f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3, then a and b are respectively

If f(x)=ax+b , where a and b are integers, f(-1)=-5 and f(3)=3 then a and b are equal to

Let a ,b in N and a > 1. Also p is a prime number. If a x^2+b x+c=p for any intergral values of x , then prove that ax^2+b x+c!=2p for any integral value of xdot

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =- and the graph of f (x) cuts y-axis at y =2. If f (x) =a has two distinct real roots, then comlete set of values of a is :

Let f(x)=x^(2)-ax+b , 'a' is odd positive integar and the roots of the equation f(x)=0 are two distinct prime numbers. If a+b=35 , then the value of f(10)=

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

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of integral value of a,a, in [-5, 5] for which the equation...

    Text Solution

    |

  2. The number of non-negative integral vlaues of n, n le 10 so that a roo...

    Text Solution

    |

  3. Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x...

    Text Solution

    |

  4. If x and y are real numbers connected by the equation 9x ^(2)+2xy+y^(2...

    Text Solution

    |

  5. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

    Text Solution

    |

  6. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

    Text Solution

    |

  7. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

    Text Solution

    |

  8. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

    Text Solution

    |

  9. Let x,y and z are positive reals and x ^(2) + xy + y ^(2)=2,y ^(2)+yz+...

    Text Solution

    |

  10. The number of ordered pairs (a,b) where a,b are integers satisfying th...

    Text Solution

    |

  11. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

    Text Solution

    |

  12. If the range of the values of a for which the roots of the equation x ...

    Text Solution

    |

  13. Find the number of positive integers satisfying the inequality x^(2) -...

    Text Solution

    |

  14. If sin theta and cos theta are the roots of the quadratic equation ax...

    Text Solution

    |

  15. Let the inequality sin ^(2) x+a cos x +a ^(2) ge1+ cos x is satisfied...

    Text Solution

    |

  16. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

    Text Solution

    |

  17. The sum of all integral values of 'a' for which the equation 2x ^(2) -...

    Text Solution

    |

  18. Let f (x) be a polynomial of degree 8 such that F(r)=1/r, r=1,2,3,…,8,...

    Text Solution

    |

  19. Let alpha, beta are two real roots of equation x ^(2) + px+ q =0, p ,q...

    Text Solution

    |

  20. If cos A, cos B and cos C are the roots of the cubic x^(3)+ax^(2)+bx+c...

    Text Solution

    |