Home
Class 12
MATHS
If f(x)=|(x+c1,x+a,x+a),(x+b,x+c2,x+a),(...

If `f(x)=|(x+c_1,x+a,x+a),(x+b,x+c_2,x+a),(x+b,x+b,x+c_3)|` then show that f(x) is linear in x. Hence deduce`f(0)= (bg(a)-ag(b))/((b-a))` where `g(x)=(c_1-x)(c_2-x)(c_3-x)`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ARIHANT MATHS|Exercise Single Option Correct Type Questions|2 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|26 Videos

Similar Questions

Explore conceptually related problems

If f(x) = |(0, x-a, x-b),(x+a, 0, x-c),(x+b, x+c, 0)| , then the value of f(0) is :

If f(x)={(x","xle1,),(x^2+bx+c",",xgt1):} then find the values of b and c if f(x) is diferentiable at x=1.

If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f(0)=0 f(1)=0

ARIHANT MATHS-DETERMINANTS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f(x)=|(x+c1,x+a,x+a),(x+b,x+c2,x+a),(x+b,x+b,x+c3)| then show that ...

    Text Solution

    |

  2. If a^(2)+b^(2)+c^(2)=-2 and f(x)= |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x...

    Text Solution

    |

  3. The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 ...

    Text Solution

    |

  4. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[logan...

    Text Solution

    |

  5. If D =|{:(1,1,1),(1,1+x,1),(1,1,1+y):}|"for" " "xne0,yne0 then D is

    Text Solution

    |

  6. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  7. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

    Text Solution

    |

  8. Let a,b,c be such that b(a+c)ne 0. If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,...

    Text Solution

    |

  9. If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):...

    Text Solution

    |

  10. The number of values of k which the linear equations 4x+ky+2z=0 kx...

    Text Solution

    |

  11. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  12. The number of values of k, for which the system of equations (k""+"...

    Text Solution

    |

  13. If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)...

    Text Solution

    |

  14. The set of the all values of lamda for which the system of linear equa...

    Text Solution

    |

  15. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

  16. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-l...

    Text Solution

    |

  17. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

  18. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

  19. If S is the set of distinct values of ' b for which the following syst...

    Text Solution

    |