Home
Class 11
MATHS
Ifbgta, then the equation (x-a)(x-b)-1=0...

If`bgta`, then the equation (x-a)(x-b)-1=0, has

A

Both the root in [a,b]

B

Both root in `(-infty,a)`

C

Both roots in `(b,infty)`

D

one root in `(-infty,a)` and other in `(b,infty)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

  • RECTANGULAR CO-ORDINATES

    PATHFINDER|Exercise QUESTION BANK|27 Videos

Similar Questions

Explore conceptually related problems

If b gt a , then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a, b) " " (b) Both roots in (-oo, a) (c) Both roots in (b, +oo) " " (d) One root in (-oo, a) and the other in (b, +oo)

If bgta , then prove that the equation (x-a)(x-b)-1=0 has one root in (-infty,a) and the other in (b,+infty) .

The equation x-2/(x-1)=1-2/(x-1) has

The equation e^(x-1)+x-2=0 as

The equation x^(2)-3|x|+2=0 has

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If alpha and beta be the roots of the equation (x-a)(x-b)=c ( cne0 ),prove that a and b are the roots of the equation (x-alpha)(x-beta)+c=0 .

Let alpha,beta be the roots of the equation (x-a)(x-b)=c, c ≠ 0. Then the roots of the equation (x-alpha)(x-beta)+c =0 are :

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has

The quadratic equations p(x) =0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has

PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
  1. The number of solutions of the equation sin(e^x)=5^x+5^(-x)is

    Text Solution

    |

  2. If p(x) be a polynomial satisfying the identity p(x^2)+2x^2+10x=2xp(x+...

    Text Solution

    |

  3. Ifbgta, then the equation (x-a)(x-b)-1=0, has

    Text Solution

    |

  4. The value of alpha and beta such that equation x^2+2x+2+e^a-sinbeta=0 ...

    Text Solution

    |

  5. The values of 'a' for which x^2+ax+sin^-1(x^2-4x+5)+cos^-1(x^2-4x+5)=...

    Text Solution

    |

  6. The number of real solution to the equation -x^2+x-1=sin^(2)x

    Text Solution

    |

  7. If 1,2,3 and 4 are the roots of the equation x^4+ax^3+bx^2+cx+d=0 then...

    Text Solution

    |

  8. The smallest positive x satisfying logsin x cos x+log(cos x) (sin x)=2...

    Text Solution

    |

  9. The set of values of 'a' for which x^2-ax+sin^-1(sin4)gt0 forallx in R...

    Text Solution

    |

  10. If (a^3(x-b)(x-c)(x-d))/((a-b)(a-c)(a-d))+(b^3(x-c)(x-d)(x-a))/((b-c)(...

    Text Solution

    |

  11. Let f(x)=x^3+3x^2+6x+2sinx, then the equation 1/(x-f(1))+2/(x-f(2))+3/...

    Text Solution

    |

  12. Integral value of x for, which (5x-1)lt(x+1)^2lt7x-3

    Text Solution

    |

  13. If exp{(sin^2 x+sin^4 x+sin^6 x+...)In2} satisfies the quadratic equat...

    Text Solution

    |

  14. The number of values of the triple (a,b,c) for which a coss 2x+bsin^2 ...

    Text Solution

    |

  15. The sum of the real roots of the equationabs(x)^2+absx-6=0 is

    Text Solution

    |

  16. If blt0, then the roots x1 and x2 of the equation 2x^2+6x+b=0, satisfy...

    Text Solution

    |

  17. If (2x^2-3x+1)(2x^2+5x+1)=9x^2,then equation has

    Text Solution

    |

  18. Ifalpha,beta are the roots of x^2+px+q=0 and also of x^(2n)+p^n x^n+q^...

    Text Solution

    |

  19. If 3^x.8^(x/(x+2))=6, then x equals.

    Text Solution

    |

  20. Value (s) of 'a' for which ax^2+(a-3)x+1lt0 for at least one positive ...

    Text Solution

    |