Home
Class 12
MATHS
If |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a...

If `|1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c),` then the solution of the equation `|1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x=-c_(x-c)(x-a)(x-a)(x-b)|=0i s`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are different, then the determinant |1 1 1(x-a)^2(x-b)^2(x-c)^2(x-b)(x-c)(x-c)(x-a)(x-a)(x-b)| vanishes when a.a+b+c=0 b. x=1/3(a+b+c) c. x=1/2(a+b+c) d. x=a+b+c

Solution of equation ((x-b)(x-c))/((a-b)(a-c))+((x-c)(x-a))/((b-c)(b-a))+((x-a)(x-b))/((c-a)(c-b))=1 is/are.

If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|= (a -b) (b -c) (c -a) (a + b+c) where a, b, c are all different, then the determinant |(1,1,1),((x-a)^(2),(x -b)^(2),(x -c)^(2)),((x -b) (x -c),(x -c) (x -a),(x -a) (x -b))| vanishes when

(x^(3))/((x-a)(x-b)(x-c))=1+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1 = (x^(3))/((x-a)(x-b)(x-c)) .

(1)/(x^(b)+x^(-c)+1)+(1)/(x^(c)+x^(-a)+1)+(1)/(x^(a)+x^(-b)+1)

RESONANCE DPP-JEE MAINS-All Questions
  1. The function f(x)=(tan^(-1)x)^3-(cot^(-1)x)^2+tan^(-1)x+2 is (a)decr...

    Text Solution

    |

  2. If the lines joining the points of intersection of the curve 4x^2+9y+1...

    Text Solution

    |

  3. If |1 1 1a b c a^3b^3c^3|=(a-b)(b-c)(c-a)(a+b+c), then the solution o...

    Text Solution

    |

  4. The equation of the circle of radius 5 in the first quadrant which ...

    Text Solution

    |

  5. If P=cospi/(20)dotcos(3pi)/(20)dotcos(7pi)/(20)dotcos(9pi)/(20)&Q=cosp...

    Text Solution

    |

  6. If alpha,alpha^2) falls inside the angle made by the lines 2y=x ,x >0&...

    Text Solution

    |

  7.   (2sec theta+3 tan theta+5 sin theta -7cos theta+5)/(2tan theta+3 s...

    Text Solution

    |

  8. If A and B are symmetric matrices then A B-B A is a Symmetric Matrix ...

    Text Solution

    |

  9. If a ,b ,c are real numbers satisfying the conditgion a+b+c=0, then th...

    Text Solution

    |

  10. If x1, x2& x3 are three distinct numbers which satisfy the relation ...

    Text Solution

    |

  11. The solution set of the inequality (3^x-4^x)/(x^2-3x-4)geq0i s

    Text Solution

    |

  12. If the lines x^2+2x y-35 y^2-4x+44 y-12=0&5x+lambday-8=0 are conc...

    Text Solution

    |

  13. If P=(sin 300^0dottan 330^0dotsec 420^0)/(tan135^0dots in 210^0dots ...

    Text Solution

    |

  14. Which of the following equations have no real solutions? (a) x^2-2x+5...

    Text Solution

    |

  15. Let y=1/(2+1/(3+1/(2+1/(3+)))) , then the value of y is (a)(sqrt(1...

    Text Solution

    |

  16. Consider a function f(x):R(R)R and if (lim)(xveca)[f(x)] does not exis...

    Text Solution

    |

  17. Number of integers satisfying the inequation (x^2-x-1)(x^2-x-7)<-5, ar...

    Text Solution

    |

  18. If the quadratic equations, a x^2+2c x+b=0a n da x^2+2b x+c=0(b!=c) ha...

    Text Solution

    |

  19. If the expression cos(x-(3pi)/2)+sing((3pi)/2+x)+sin(32pi+x)-18cos(19...

    Text Solution

    |

  20. Domain of f(x)=sin^(-1)[2-4x^2], where [.] denotes the greatest intege...

    Text Solution

    |