Home
Class 12
MATHS
Let a ,b in na n a > 1. Also p is a pri...

Let `a ,b in na n 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 `a+b x+c!=2p` for any integral value of `xdot`

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos

  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

Similar Questions

Explore conceptually related problems

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

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 X ~ B (6,p) and 2. P (X =3) =P (X= 2) then find the value of p

Let a,b, c be unequal real numbers.If a,b,c are in G.P.and a+b+c=bx, then 'x' can not lie in

If a,b,c are in G.P and a+x,b+x,c+x are in H.P,then the value of x is (a,b,c are distinct numbers)

If a, b, c are in A.P. and a, x, b, y, c are in G.P., then prove that b^(2) is the arithmatic mean of x^(2)" and "y^(2).

Let p = 144 ^(sin^(2)x) + 144^( cos^(2)x), then the number of integral values of such p's can take are

If a, b, c are in A.P. and x, y, z are in G.P., then prove that : x^(b-c).y^(c-a).z^(a-b)=1

Let P(x)=ax^(2)+bx+8 is a quadratic polynomial. If the minimum value of P(x) is 6 when x=2 , find the values of a and b.

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If altbltcltd the equation (x-a)(x-c)+lambda(x-b)(x-d)=0 has real root...

    Text Solution

    |

  2. If p is the first of the n arithmetic means between two numbers and q ...

    Text Solution

    |

  3. Let a ,b in na n a > 1. Also p is a prime number. If a x^2+b x+c=p fo...

    Text Solution

    |

  4. Given two quadratic equation x^2-x+m=0 and x^2-x+3m=0, m!=0. Find the ...

    Text Solution

    |

  5. If a, b, c are in HP, find the relation between the roots of ax^2+bx+c...

    Text Solution

    |

  6. Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbet...

    Text Solution

    |

  7. For what values of m epsilonR, both roots of the equation x^(2)-6mx+9m...

    Text Solution

    |

  8. If ax^2-bx + c=0 have two distinct roots lying in the interval (0,1); ...

    Text Solution

    |

  9. The set of values of a for which the inequality, x^2 + ax + a^2 + 6a ...

    Text Solution

    |

  10. Find all integral values of a for which the quadratic expression (x - ...

    Text Solution

    |

  11. Find the values of the parameter a for which 4^x-a.2^x-a+3 <= 0 for at...

    Text Solution

    |

  12. Find all values of the parameter a for which the inequality a.9^x +4(a...

    Text Solution

    |

  13. Solve the equation sqrt(a(2x^x-2)+1)=1-2^x ,x in Rdot

    Text Solution

    |

  14. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

    Text Solution

    |

  15. The sum of all the integral value(s) of k in [0, 15] for which the ine...

    Text Solution

    |

  16. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

    Text Solution

    |

  17. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

    Text Solution

    |

  18. If f(x)=x^2+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(...

    Text Solution

    |

  19. If a, b, c are in GP, then the equations ax^2 +2bx+c = 0 and dx^2 +2ex...

    Text Solution

    |

  20. Show that the minimum value of (x+a)(x+b)//(x+c)dotw h e r ea > c ,b >...

    Text Solution

    |