Home
Class 12
MATHS
If b ge a, then the equation (x-a)(x-b)-...

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

A

1: both the roots in `[a, b]`

B

2: both the roots in `(-oo, a]`

C

3: both roots in `(b, oo]`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos

  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

If a le b le c le d then the equation (x-a)(x-c)+2(x-b)(x-d)=0 has

If |a|<|b|,b-a<1 and a,b are the real roots of the equation x^2-|alpha|x-|beta|=0, then the equation log_(|b|)|x/a|-1=0 has

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

Let f(x)=a x^(2)+b x+c , a, b, in R, a neq 0 satisfying f(1)+f(2)=0 . Then the equation f(x)=0 has

If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a root in

If a, b and c are distinct real numbers, prove that the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has real and distinct roots.

If the quadratic equation (b-c)x_2+(c-a)x+(a-)=0 has equal roots, then show that 2b=a+c .

If the quadratic equation (b-c)x_2+(c-a)x+(a-b)=0 has equal roots, then show that 2b=a+c .

Show that the equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 has no real roots when a!=b .

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. In a triangle PQR, /R = pi//2, If tan(P//2). and tan(Q//2) are the roo...

    Text Solution

    |

  2. If the roots of the equation x^(2) - 2ax + a^(2) + a - 3 = 0 are real ...

    Text Solution

    |

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

    Text Solution

    |

  4. For the equation 3 x^(2)+p x+3=0, p gt 0, if one root is square of the...

    Text Solution

    |

  5. If x^(2)+(a-b) x+(1-a-b)=0, a, b in R has unequal roots for all values...

    Text Solution

    |

  6. If one root of the equation x^(2) + px + q = 0 is square of the other...

    Text Solution

    |

  7. If x^(2)+2 a x+(10-3 a) gt 0 for all x, then

    Text Solution

    |

  8. Let f(x)=a x^(2)+b x+c, a ne 0 and Delta=b^(2)-4 a c . If alpha+beta, ...

    Text Solution

    |

  9. Let a,b,c be the sides of a triangle no two of them are equal and la...

    Text Solution

    |

  10. If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...

    Text Solution

    |

  11. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and (alpha)/...

    Text Solution

    |

  12. The smallest value of k for which both the roots of the equation x^(2)...

    Text Solution

    |

  13. The minimum positive value of (x^(2)+2 x+4)/(x+2) is

    Text Solution

    |

  14. Let p and q be real number such that p ne 0 , p^(3) ne q and p^(3...

    Text Solution

    |

  15. If p and q are the roots of the equation x^(2)+p x+q=0 then

    Text Solution

    |

  16. If the difference between the roots of x^(2)+a x+b=0 is same as that o...

    Text Solution

    |

  17. If alpha ne beta and alpha^(2) = 5 alpha - 3, beta^(2) = 5 beta - 3 , ...

    Text Solution

    |

  18. The number of real roots of the equation |x|^(2)-3|x|+2=0 is

    Text Solution

    |

  19. If one root of the equation x^(2)+p x+12=0 is 4, while the equation x^...

    Text Solution

    |

  20. If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a...

    Text Solution

    |