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

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)`

A

both roots in [a,b]

B

both roots in `(-oo,oo)`

C

both roots in `(0,oo)`

D

one root in `(-oo,oo)` and other in `(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Main ( Archive )|20 Videos

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos

  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos

  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

If bgta then show that the equation (x-a)(x-b)-1=0 has one root less than a and other root greater than b.

If 0ltalphalt pi/4 equation (x-sinalpha)(x-cosalpha)-2=0 has (A) both roots in (sinalpha, cosalpha) (B) both roots in (cosalpha, sinalpha) (C) one root in (-oo, cosalpha) and other in (sinalpha, oo) (D) one root in (-oo,sinalpha) and other in (cosalpha, oo)

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

If one root of the equation 2x^2+k x-6=0 is 2, then the other root is (a) 6 (b) -6 (c) -1 (d) 1

If one root of the equation x^2+a x+3=0 is 1, then the other root is (a) 3 (b) -3 (c) 2 (d) -2

If p,q be non zero real numbes and f(x)!=0, x in [0,2] also f(x)gt0 and int_0^1 f(x).(x^2+px+q)dx=int_1^2 f(x).(x^2+px+q)dx=0 then equation x^2+px+q=0 has (A) two imginary roots (B) no root in (0,2) (C) one root in (0,1) and other in (1,2) (D) one root in (-oo,0) and other in (2,oo)

both roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are

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 a and b are roots of the equation x^2+a x+b=0 , then a+b= (a) 1 (b) 2 (c) -2 (d) -1

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -LEVEL -2
  1. The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + ...

    Text Solution

    |

  2. if both root of equation x^2-6ax+2-2a+9a^2 = 0 exceeds 3 . then show t...

    Text Solution

    |

  3. If b gt a, then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a...

    Text Solution

    |

  4. which of the following graph represents the expression f(x) = ax^2 + b...

    Text Solution

    |

  5. If alpha, beta are the roots of the equation (x-a)(x-b)=c,c!=0. Find t...

    Text Solution

    |

  6. Let alpha ,beta " be the roots of " ax^(2) +bx + c= 0, gamma, detla ...

    Text Solution

    |

  7. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  8. If alpha , beta are roots of ax^(3) +bx +c=0 then the equation ax^...

    Text Solution

    |

  9. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  10. The polynomiaal (a x^2+b x+c)(a x^2-dx-c), a c!=0 has

    Text Solution

    |

  11. If the equation ax^(2)+2bx-3c=0 has no real roots and ((3c)/(4))lta+b,...

    Text Solution

    |

  12. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  13. If alpha and beta(alpha lt beta) are the roots of the equation x^(2)+b...

    Text Solution

    |

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

    Text Solution

    |

  15. If the roots of a1x^(2)+b1x+c1=0 and alpha1 , beta1 and those of a2...

    Text Solution

    |

  16. If b^2>4ac, then a(x^2 +4x+4)^2+b(x^2 +4x +4)+c=0 has distinct real ...

    Text Solution

    |

  17. If ( lambda^(2) + lambda - 2)x^(2)+(lambda+2)x lt 1 for all x in R ,...

    Text Solution

    |

  18. The value of k for which the equation (k-2) x^(2) + 8x + k + 4 = 0 has...

    Text Solution

    |

  19. For all x in R if mx^(2) - 9mx + 5m + 1 gt 0 , then m lies in the in...

    Text Solution

    |

  20. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |