Home
Class 12
MATHS
The number of integral values of a for w...

The number of integral values of a for which the quadratic equation `(x+a)(x+1991)+1=0` has integral roots are a. 3 b. 0 c. 1 d. 2

A

3

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
4
`(x + a)(x + 1991) + 1 = 0`
or `(x + a)(x + 1991) = -1`
`rArr (x + a) = 1 and x + 1991 = -1`
`rArr a = 1993`
or `x + a = -1 and x + 1991 = 1 rArr a = 1989`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.13|9 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

The number of integral values of 'a' for which the quadratic equation x^(2)+(a+19)x+19a+1=0 has integral roots,are

Integral value(s) of a such that the quadratic equation x^(2)+ax+a+1=0 has integral roots is/are

Number of integral values of a for which the equation x^(2)-(a+1)x+a-1=0, has integral roots,is equal to -

The sum of all integral values of 'a' for which the equation 2x ^(2) -(1+2a) x+1 +a=0 has a integral root.

Find the value of k for which the quadratic equations (k+1)x^(2)+2(k-1)x+1=0 has equal roots

Number of possible value(s) of integer 'a' for which the quadratic equation x^(2) + ax + 16 = 0 has integral roots, is

Number of integral values of a for which quadratic equation (a-1)x^(2)+(4a+1)x-6=0 have both roots integer,is

CENGAGE-THEORY OF EQUATIONS-Exercise (Single)
  1. Consider the equation x^(2) + 2x - n = 0m where n in N and n in [5, 10...

    Text Solution

    |

  2. Number of integral values of a for which the equation x^2-(a+1)x+a-1=0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. The number of real solutions of |x|+2sqrt(5-4x-x^2)=16 is/are a. 6 ...

    Text Solution

    |

  6. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  7. If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^3+...

    Text Solution

    |

  8. If (mr ,1//mr),r=1,2,3,4, are four pairs of values of xa n dy that sat...

    Text Solution

    |

  9. If roots of an equation x^n-1=0 are 1,a1,a2,........,a(n-1) then the v...

    Text Solution

    |

  10. If tantheta1,tantheta2,tantheta3 are the real roots of the x^2-(a+1x^2...

    Text Solution

    |

  11. If alpha,beta,gamma are the roots of x^3-x^2-1=0 then the value of (1+...

    Text Solution

    |

  12. If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3K x^2...

    Text Solution

    |

  13. Set of all real value of a such that f(x)=((2a-1)+x^2+2(a+1)x+(2a-1))/...

    Text Solution

    |

  14. If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imagi...

    Text Solution

    |

  15. If he expression [m x-1+(1//x)] is non-negative for all positive real ...

    Text Solution

    |

  16. Suppose that f(x) isa quadratic expresson positive for all real xdot I...

    Text Solution

    |

  17. Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(...

    Text Solution

    |

  18. Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R. T...

    Text Solution

    |

  19. Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real...

    Text Solution

    |

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

    Text Solution

    |