Home
Class 11
MATHS
For real x , the function (x-a)(x-b)//(x...

For real `x ,` the function `(x-a)(x-b)//(x-c)` will assume all real values provided `a > b > c` b. `a c > b` d. `a

A

`a le c le b`

B

`b ge a ge c`

C

`b le c le a`

D

`a ge b ge c`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

For real x, the function ((x-a)(x-b))/(x-c) will assume all real values provided a) agtbgtc b) altbltc c) agtc ltb d) a le c le b

Prove that if x is real, the expression ((x-a)(x-c))/(x-b) is capable of assuming all values if agtbgtc or altbltc .

If a ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is a. all real and is distinct b. all real and at least two are distinct c. at least two real d. all non-real

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

If a,b,c,d are unequal positive numbes, then the roots of equation x/(x-a)+x/(x-b)+x/(x-c)+x+d=0 are necessarily (A) all real (B) all imaginary (C) two real and two imaginary roots (D) at least two real

If a, b, c are real then (b-x)^(2)-4(a-x) (c-x)=0 will have always roots which are

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. Root of the quadratic equation x^2+6x-2=0

    Text Solution

    |

  2. If sum of the roots of ax^(2)+bx+c=0 is equal to the sum of the square...

    Text Solution

    |

  3. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

    Text Solution

    |

  4. 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

    |

  5. If the roots of the equation a x^2+2b x+c=0 and b x^2-2sqrt(a c) x+b=0...

    Text Solution

    |

  6. If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b,...

    Text Solution

    |

  7. if p and q are non zero constants, the equation x^2+px+q=0 has roots ...

    Text Solution

    |

  8. The equation x^((3)/4 (log2x)^2+log2 x -(5)/(4))=sqrt(2) has :

    Text Solution

    |

  9. cosα is a root of the equation 25x^2+5x−12=0,−1 lt x lt 0, then the va...

    Text Solution

    |

  10. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

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

    Text Solution

    |

  12. If a,b,c epsilonQ then roots of the equation (b+c-2a)x^(2)+(c+a-2b)x+(...

    Text Solution

    |

  13. If a,b,c are positive real numbers, then the number of real roots of t...

    Text Solution

    |

  14. Real roots of equation x^2 + 5 |x| + 4 = 0 are

    Text Solution

    |

  15. If aa n db(!=b) are the roots of the equation x^2+a x+b=0, then find t...

    Text Solution

    |

  16. If f(x) = (x^2 -2x + 4)/(x^2+2x+4), x in R then range of function is

    Text Solution

    |

  17. If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0...

    Text Solution

    |

  18. If alpha, beta are the roots of the quadratic equation x^2 + bx - c = ...

    Text Solution

    |

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

    Text Solution

    |

  20. If alpha ne beta but alpha^(2)= 5 alpha - 3 and beta ^(2)= 5 beta...

    Text Solution

    |