Home
Class 12
MATHS
If a ,b ,c are distinct positive numbers...

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 all real and is distinct all real and at least two are distinct at least two real d. all non-real

A

all real and distinct

B

all real and atleast two are distinct

C

atleast two real

D

all non - real

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|20 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - I|3 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|28 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

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 real and is distinct b.all real and at leat two are distinct c.at least two real d.all non-real

If a,b,c are distinct positive real numbers, then

If a,b,c are positive real numbers,then the number of real roots of the equation ax^(2)+b|x|+c is

If a,b,c are positive real numbers.then the number of real roots of the equation ax^(2)+b|x|+c=0 is

For three distinct real numbers a,b,c, the number of real roots of the equation (x-a)^(3)+(y-b)^(3)+(z-c)^(3)=0

The number of the distinct real roots of the equation (x+1)^(5)=2(x^(5)+1)

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

FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. The number of real solutions of the equation sin (e^x)= 5^x+5^-x

    Text Solution

    |

  2. The equation (x-3)^9+(x-3^2)^9+(x-3^3)^9+.....+(x-3^9)^9=0 has

    Text Solution

    |

  3. The set of all real numbers x for which x^2-|x+2| +x gt 0 is

    Text Solution

    |

  4. The exhaustive set of values of a for which the equation a sin(x+(pi)/...

    Text Solution

    |

  5. If the roots of the equation (a)/(x+a+k)+(b)/(x+b+k)=2 are equal in ma...

    Text Solution

    |

  6. The set of all x in the interval [0, pi] for which 2 sin^(2)x-3 sin x ...

    Text Solution

    |

  7. Let a gt 0, b gt 0 then both roots of the equation ax^(2)+bx+c=0

    Text Solution

    |

  8. The number of positive integral solutions of x^4-y^4=3789108 is 0 b. 1...

    Text Solution

    |

  9. The set of values for which x^(3)+1 ge x^(2)+x is

    Text Solution

    |

  10. If a ,b ,c are distinct positive numbers, then the nature of roots of ...

    Text Solution

    |

  11. If roots of the equation x^2-2ax+a^2+a-3=0 are real and less than 3 t...

    Text Solution

    |

  12. If a(1), a(2), a(3)(a(1)gt 0) are in G.P. with common ratio r, then th...

    Text Solution

    |

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

    Text Solution

    |

  14. If alpha and beta are the roots of x^(2)-3px+p^(2)=0 such that alpha^(...

    Text Solution

    |

  15. The number of solutions of the equation n^(-|x|)|m-|x||=1 (where m, n ...

    Text Solution

    |

  16. If (m^2-3)x^2+3mx+ 3m+1=0 has roots which are reciprocals of each othe...

    Text Solution

    |

  17. If the two equation x^(2)-cx+d=0 and x^(2)-ax+b=0 have one common root...

    Text Solution

    |

  18. If the inequality (m x^2+3x+4+2x)//(x^2+2x+2)<5 is satisfied for all x...

    Text Solution

    |

  19. If one of the roots of the equation 2x^(2)-6x+k=0 is (alpha + 5i)/(2) ...

    Text Solution

    |

  20. For all 'x', x^(2)+2ax+10-3a gt 0, Statement 1 : the interval in wh...

    Text Solution

    |