Home
Class 12
MATHS
The integral values of x for which x^(2)...

The integral values of x for which `x^(2)+7x+13` is perfect square are `alpha and beta` then

A

`alpha and beta` are -ve integer

B

`alpha^(2)+beta^(2)` is perfect square of an iteger

C

atleast one of the value `alpha or beta` is negative

D

atleast one of the value `alpha or beta` is prime

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos
  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

The integral values of x for which x^(2)+17x+71 is perfect square of a rational number are a and b,then |a-b|=

If the positive integral values of x for which f(x)=x^(3)-8x^(2)+20x-13 is a prime are alpha,beta,gamma then

The value of 'c' for which |alpha^(2) - beta^(2)| = 7//4 , where alpha and beta are the roots of 2 x^(2) + 7 x + c = 0 , is

Find all integral values of a for which the quadratic expression (x-a)(x-10)+1 can be factored as a product (x+alpha)(x+beta) of two factors and alpha,beta in I.

If alpha,beta are the values of x for which {x},[x],x are in harmonic progression then find the value of (1)/(| alpha beta|)

The number of values of 'a' for which {x^(2) -(a-2) x+ a^(2)} {x^(2) + ax + (2a -1)} is a perfect square, is

If alpha and beta are the roots of the equation x^(2)+alpha x+beta=0 such that alpha ne beta , then the number of integral values of x satisfying ||x-beta|-alpha|lt1 is

The least prime integral value of '2a' such that the roots alpha,beta of the equation 2x^(2)+6x+a=0 satisfy the inequality (alpha)/(beta)+(beta)/(alpha)<2 is

Let alpha , beta be roots of x^(2) + x +1 = 0 , then the equation whose roots are (alpha)^10 and (beta)^13 is

If a, ß are the zeroes of the polynomial f(x) = x^2 - 7x + 12 , then find the value of 1/alpha + 1/beta .

RESONANCE-DPP-QUESTION
  1. sin 300°. tan 330°. sec 420° tan 135°. sin 210°. sec 315 sec 480°. cos...

    Text Solution

    |

  2. For m in R, let f(x) =x^(3)+3mx^(2)-3x-3m+2"has 3 real roots" x(1),x(2...

    Text Solution

    |

  3. The integral values of x for which x^(2)+7x+13 is perfect square are a...

    Text Solution

    |

  4. The number of integral values of a for which the quadratic equation (x...

    Text Solution

    |

  5. If both roots of the equation a(x^2-1)+x+c are imaginary and c gt -1 t...

    Text Solution

    |

  6. Find the number of integral values of 'a' for which ax^2 - (3a + 2)x +...

    Text Solution

    |

  7. Let X1, X2, x3 be 3 roots of the cubic x^3 – X-1 = 0. Then the exp...

    Text Solution

    |

  8. for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

    Text Solution

    |

  9. If the difference between the corresponding roots of x^(2)+ax+b=0and x...

    Text Solution

    |

  10. The number of roots of the equation, x-(2)/(x-1) is

    Text Solution

    |

  11. If sin thetaand cos theta are the roots of the equation ax^(2)-bx+c=0,...

    Text Solution

    |

  12. Number of integral value (s) of 'x' satisfying the equation log(1/5)(s...

    Text Solution

    |

  13. The set (A uu B')uu(B nn C) is equal to

    Text Solution

    |

  14. The set (A uu B')uu(B nn C) is equal to

    Text Solution

    |

  15. If n(AuuBuuC)+n(AuuBuuC)'=50,n(A)=10,n(B)=15,n(C)=20,n(AnnB)=5,n(BnnC)...

    Text Solution

    |

  16. If A={2,3,4,8,10}.B={3,4,5,10,12},C={4,56,12,14}then(AnnB)uu(AnnC) is ...

    Text Solution

    |

  17. If A={1,3,5,7,9,11,13,15,17}, B={2,4,.......,18} and N the set of natu...

    Text Solution

    |

  18. Of the number of three athletic teams in a school, 21 are in the baske...

    Text Solution

    |

  19. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  20. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

    Text Solution

    |