Home
Class 12
MATHS
Both the roots of the equation (x-b)(x-c...

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

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

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise LEVEL -2|64 Videos
  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos
  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos
  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 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 are real, then 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) imaginary.

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

Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c) (x -a) =0 are always real and these cannot be equal unless a=b=c

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

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

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

Show that the roots of (x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0 are real, and that they cannot be equal unless a=b=c.

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -JEE Advance ( Archive )
  1. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are ...

    Text Solution

    |

  2. Let alpha, beta be the roots of the equationpx^(2)+qx+r=0, p!=0. If p,...

    Text Solution

    |

  3. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

    Text Solution

    |

  4. Let a,b,c be the sides of a triangle. Now two of them are equal to lam...

    Text Solution

    |

  5. If alpha and beta are the roots of the equation x^2+ax+b=0 and alpha^4...

    Text Solution

    |

  6. The sum of all real values of x satisfying the equation (x^(2) -5x+5)...

    Text Solution

    |

  7. Let a and b are the roots of the equation x^2-10 xc -11d =0 and those...

    Text Solution

    |

  8. If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,be...

    Text Solution

    |

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

    Text Solution

    |

  10. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

    Text Solution

    |

  11. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

    Text Solution

    |

  12. If a in R and the equation =-3(x-[x])^(2)+2(x-[x])+a^(2)=0 (where [x...

    Text Solution

    |

  13. If x^(2) + (a - b) x + (1 - a - b) = 0, where a , b in R , then find ...

    Text Solution

    |

  14. Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbet...

    Text Solution

    |

  15. The smallest value of k for which both roots of the equation x^(2)-8kx...

    Text Solution

    |

  16. Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...

    Text Solution

    |

  17. Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,...

    Text Solution

    |

  18. Let (x(0), y(0)) be the solution of the following equations: (2x)^("...

    Text Solution

    |

  19. If 3^(x)=4^(x-1), then x is equal to

    Text Solution

    |

  20. The value of 6+ log(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sq...

    Text Solution

    |

  21. The largest interval for whichx^(12)+x^9+x^4-x+1>0 -4<xlt=0 b. 0<x<1 ...

    Text Solution

    |