Home
Class 12
MATHS
Both the roots of the equation : (x -...

Both the roots of the equation :
(x - b) (x -c) + (x - c) (x - a) + (x - a) (x - b) = 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

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos

  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are real and a!=b , then the roots of the equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

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

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

Let alpha, beta the roots of the equation (x - a) (x - b) = c , c ne 0. Then the roots of the equation (x - alpha ) x - beta) + c = 0 are :

Let a, b,c be sides of a triangle. No two of them are equal and lambda in R. If the roots of the equation x^(2) + 2 (a + b + c) x + 3 lambda (ab + bc + ca ) = 0 are real , then :

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 the roots of the equations (b-c) x^(2) + (c-a) x+( a-b) =0 are equal , then prove that 2b=a+c

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

The root of the equation : |(a-x,b,c),(0,b-x,0),(0,b,c-x)|=0 are :

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. Let alpha, beta the roots of the equation (x - a) (x - b) = c , c ne...

    Text Solution

    |

  2. If a le b le c le d then the equation (x-a)(x-c)+2(x-b)(x-d)=0 has

    Text Solution

    |

  3. Both the roots of the equation : (x - b) (x -c) + (x - c) (x - a) +...

    Text Solution

    |

  4. If one root of the equation (a-b) x^(2)+a x+1=0 is double the other an...

    Text Solution

    |

  5. If alpha,beta be the roots of x^(2)+x+2=0 and gamma, delta be the root...

    Text Solution

    |

  6. The expression a (x^(2)-y^(2))-b x y admits two linear factors for

    Text Solution

    |

  7. If one root of x^(2)-x-k=0 is square of the other, then k=

    Text Solution

    |

  8. The value of p for which the difference between the roots of the equat...

    Text Solution

    |

  9. If one root of the equation ax^(2) + bx + c =0 is reciprocal of the o...

    Text Solution

    |

  10. If one root of the equation 5 x^(2)+13 x+k=0 is reciprocal of other, t...

    Text Solution

    |

  11. Let f(x)=a x^(2)+b x+c, a, b, in R, a neq 0 satisfying f(1)+f(2)=0 . T...

    Text Solution

    |

  12. If the roots of a x^(2)+b x+c=0(a ge 0) be each greater than unity, th...

    Text Solution

    |

  13. If a in Z and the equation (x-3)(x-a)+1=0 has integral roots, then the...

    Text Solution

    |

  14. If the equations x^(2)+b^(2)=1-2b x and x^(2)+a^(2)=1-2 a x have one a...

    Text Solution

    |

  15. The number of values of a such that x^(2)-11 x+a and x^(2)-14 x+2 a ha...

    Text Solution

    |

  16. If the equations a x^(2)+2 b x+c-0 and a x^(2)+2 c x+b=0, b ne c have ...

    Text Solution

    |

  17. If the equations x^(2)+a x+b=0 and x^(2)+b x+a=0(a ne b) have a common...

    Text Solution

    |

  18. If x^(2)-p x+q=0 has equal integral roots, then

    Text Solution

    |

  19. Find the condition that quadratic equations x^(2)+ax+b=0 and x^(2)+bx+...

    Text Solution

    |

  20. If both roots of the equation x^(2)-2 a x+a^(2)-1= 0 lie between -2 an...

    Text Solution

    |