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

If `|[1 1 1];[a b c];[ a^3b^3c^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`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If (x-a)^(3)+(x-b)^(3)+(x-c)^(3)-3(x-a)(x-b)(x-c)=0 , then x =

If 3x = a + b + c , then find the value of (x-a)^(3)+(x-b)^(3)+(x-c)^(3)-3(x-a)(x-b)(x-c)

If F(x)=((x-b)(x-c))/((a-b)(a-c))+((x-c)(x-a))/((b-c)(b-a))+((x-a)(x-b))/((c-a)(c-b)) , show that F(0)=1.

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

If a ,b ,c are different, then the value of x satisfying |[0,x^2-a, x^3-b],[ x^2+a,0,x^2+c],[ x^4+b, x-c,0]|=0 is a. c b. a c. b d. 0

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

(1)/(x^(b)+x^(-c )+1)+(1)/(x^(c )+x^(-a)+1)+(1)/(x^(a)+x^(-b)+1) given a+b+c=0

If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of degree <3, then prove that (dg(x))/(dx)=|1af(a)(x-a)^(-2)1bf(b)(x-b)^(-2)1cf(c)(x-c)^(-2)|/|a^2a1b^2b1c^2c1|

If y=(ax^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1 , then prove that (y')/y=1/x[a/(a-x)+b/(b-x)+c/(c-x)]

Simplify : (x^(a+b).x^(a-b).x^(c-2a))/(x^(c-a)) .

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Find the following system of equations is consistent, (a+1)^3x+(a+2)...

    Text Solution

    |

  2. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

    Text Solution

    |

  3. If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b...

    Text Solution

    |

  4. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

    Text Solution

    |

  5. The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal ...

    Text Solution

    |

  6. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

    Text Solution

    |

  7. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

    Text Solution

    |

  8. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

    Text Solution

    |

  9. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

    Text Solution

    |

  10. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

    Text Solution

    |

  11. If g(x)=(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of de...

    Text Solution

    |

  12. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

    Text Solution

    |

  13. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

    Text Solution

    |

  14. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

    Text Solution

    |

  15. Which of the following has/have value equal to zero? |[8, 2, 7],[ 12, ...

    Text Solution

    |

  16. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  17. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

    Text Solution

    |

  18. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

    Text Solution

    |

  19. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

    Text Solution

    |

  20. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

    Text Solution

    |