Home
Class 12
MATHS
If a,b and c are real numbers then the r...

If a,b and c are real numbers then the roots of the equation `(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0` are always

A

positive

B

negative

C

real

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 2 (True And False)|4 Videos

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 2 (Fill In The Blanks)|3 Videos

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Problem Set - 1 (Fill In The Blanks)|4 Videos

  • THE PARABOLA

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE (Assertion/ Reason)|1 Videos

  • TRIGONOMETRICAL EQUATIONS

    ML KHANNA|Exercise SELF ASSESSMENT TEST |27 Videos

Similar Questions

Explore conceptually related problems

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

If the roots of the equation (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are equal then

-If a,b,c in R then prove that the roots of the equation (1)/(x-a)+(1)/(x-b)+(1)/(x-c)=0 are always real cannot have roots if a=b=c

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

If the roots of (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal then show that a=b=c

ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 2
  1. If the roots of the equation (x-b) (x-c) + (x-c) (x-a) + (x-a) (x-b)=0...

    Text Solution

    |

  2. If the expression x^(2)-2 (Sigma a) x+3 Sigma ab=0 be a perfect square...

    Text Solution

    |

  3. If a,b and c are real numbers then the roots of the equation (x-a)(x-b...

    Text Solution

    |

  4. If three distinct positive numbers a, b, care in H.P.,then the equatio...

    Text Solution

    |

  5. Find the condition if the roots of a x^2+2b x+c=0a n db x^2-2sqrt(a c ...

    Text Solution

    |

  6. if a lt c lt b, then check the nature of roots of the equation (a ...

    Text Solution

    |

  7. The value of m for which the equation x^(3)-mx^(2)+3x-2=0 has two root...

    Text Solution

    |

  8. If a in Z and the equation (x-a) (x-10) +1=0 is integral roots, then t...

    Text Solution

    |

  9. The equation (6-x)^(4)+(8-x)^(4)=16 has

    Text Solution

    |

  10. If x^(2)+x+1 is a factor of ax^(3)+bx^(2)+cx+d, then the real root of ...

    Text Solution

    |

  11. Let f(x) = ax^(3) + 5x^(2) - bx + 1. If f(x) when divide by 2x + 1 lea...

    Text Solution

    |

  12. If x^3+3x^2-9x=c is of the form (x-alpha)^2(x-beta) , then c is equal ...

    Text Solution

    |

  13. If the two roots of the euqation (lamda-1) (x^(2)+x+1)^(2)-(lamda+1)(x...

    Text Solution

    |

  14. The value of a for which the quadratic equation 3x^(2) + 2a^(2) + 1x...

    Text Solution

    |

  15. If 1 lies between the roots of the equation 3x^(2)-3 sin alpha x -2 co...

    Text Solution

    |

  16. If a.4^(tan x)+ a.4^(-tan x) -2=0 has real solutions, where 0 le x le ...

    Text Solution

    |

  17. If the equation (cos theta - 1) x^(2) + (cos theta ) x + sin theta =0 ...

    Text Solution

    |

  18. If the roots of the equation (x-p) (x-q) =p^(2)- 2q^(2) be real and di...

    Text Solution

    |

  19. The value of a for which the equation 2x^(2)-2(2a+1) x+a(a-1)=0 has ro...

    Text Solution

    |

  20. Find the valuesof m for which exactly one root of the equation x^(2)-2...

    Text Solution

    |