Home
Class 12
MATHS
IF (x-a)(x-b) +(x-b) (x-c) +(x-a)(x-c...

IF `(x-a)`(x-b) +(x-b) (x-c) +(x-a)(x-c)` =0 has equal roots then the relation between a , b and c is

A

a+b+c=0

B

a=b=c

C

`b^2 =ac`

D

`a+c =2b`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B (QUADRATIC EXPRESSIONS)|106 Videos

  • QUADRATIC EXPRESSIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 ( SPECIAL TYPE QUESTIONOS ) ( SET -1)|4 Videos

  • QUADRATIC EXPRESSIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 ( SPECIAL TYPE QUESTIONOS ) ( SET -4)|4 Videos

  • PROPERTIES OF TRIANGLES

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) Set-4|10 Videos

  • RELATIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise Exercise|49 Videos

Similar Questions

Explore conceptually related problems

(x^(3))/((x-a)(x-b)(x-c))

The roots of (x-b)(x-c) +(x-a)(x-c) +(x-a) (x-b)=0 are

((x-a)(x-b))/((x-c)(x-d))=A/(x-c)-B/(x-d)+C rArr C=

IF the roots of (b-c) x^2+ (c-a) x+ (a-b) =0 are equal then a, b,c are in

Show that (a^2) /( x- alpha) +( b^2)/( x -beta) +(c^2)/( x- gamma)- x + delta =0 has only real roots if a ,b,c , alpha , beta , gamma , delta are all real .

IF the roots of a(b-c)x^2+b (c-a) x+c (a-b) =0 are equal then a, b, c are in

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

If (x + 2)(x + 3b) = c has roots alpha,beta , then the roots of (x + alpha)(x+beta) + c = 0 are

DIPTI PUBLICATION ( AP EAMET)-QUADRATIC EXPRESSIONS-EXERCISE 1A (QUADRATIC EQUATIONS)
  1. IF the roots of x^2-2(5 + 2k ) x+ 3 (7+10k) are equal then ...

    Text Solution

    |

  2. If the quadratic expression x^2 -(a-1) x+ (a+ (1)/(4) ) will be...

    Text Solution

    |

  3. IF (x-a)(x-b) +(x-b) (x-c) +(x-a)(x-c) =0 has equal roots then ...

    Text Solution

    |

  4. If c^(2) ne ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If p(q-r) x^2 +q(r-p) x+r(p-q) =0 has equal roots then 2/q =

    Text Solution

    |

  8. IF the roots of (b-c) x^2+ (c-a) x+ (a-b) =0 are equal then ...

    Text Solution

    |

  9. IF the roots of a(b-c)x^2+b (c-a) x+c (a-b)=0 are equal then a, ...

    Text Solution

    |

  10. If the roots of (a^2+b^2 ) x^2 -2b(a+c)x+(b^2 +c^2 ) =0 are equal...

    Text Solution

    |

  11. IF the sum of the roots of ax^2+bx+c=0 is equal to the sum of the squa...

    Text Solution

    |

  12. IF alpha , beta are the roots of the equation ax^2 + bx +c=0 ...

    Text Solution

    |

  13. IF 3+ 4i is a root of the equation x^2 +px +q=0 then

    Text Solution

    |

  14. IF 3+i is a root of the equation x^2 + ax + b=0 then a=

    Text Solution

    |

  15. IF one root of the quadratic equation ax^2+bx +c=0 is 3-4i the...

    Text Solution

    |

  16. IF (1-p) is a root of quadratic equation X^2 +px +(1-p)=0 the...

    Text Solution

    |

  17. IF one root of the equation x^2 +px +12=0 is 4, while the equat...

    Text Solution

    |

  18. If x^(2)-6x+5=0 and x^(2)-12x+p=0 have a common root, then find p.

    Text Solution

    |

  19. If x^2-hx - 21 =0 , x^2 - 3hx +35 =0 have a common root then h=

    Text Solution

    |

  20. The value of a such that x^2 -11x+a =0 ,x^2 -14 x + 2a=0 may h...

    Text Solution

    |