Home
Class 12
MATHS
Using Properties of determinants, solve ...

Using Properties of determinants, solve the following for x:
`{:|(x+a,x,x),(x,x+a,x),(x,x,x+a)|=0`

Text Solution

Verified by Experts

The correct Answer is:
`- a/3`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTION -II)|3 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC-2 SOLUTIONS OF SYSTEM OF LINEAR EQUATIONS (LONG ANSWER TYPE QUESTIONS -II )|24 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (SHORT ANSWER TYPE QUESTIONS-II)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos

  • DIFFERENTIAL EQUATIONS

    OSWAAL PUBLICATION|Exercise HOMOGENEOUS DIFFERENTIAL EQUATIONS (Long Answer Type Questions - III)|8 Videos

Similar Questions

Explore conceptually related problems

Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2x,x+lamda,2x),(2x,2x,x+lamda)|=(5x+lamda)(lamda-x)^2

Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)|=x^3

Solve the equation {:|( x+a,x,x),(x,x+a,x),(x,x,x+a) |:}=0,ane 0

By using properties of determinants , show that : {:|( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) |:} =( 1-x^(3)) ^(2)

Using the property of determinants and without expanding {:|( x,a,x+a),( y,b,y+b),(z,c,z+c)|:} =0

Solve the following quadratic for x: 4x^(2)-4a^(2)x+(a^(4)-b^(4))=0

A root of the equation |(0, x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 is

Solve the following using quadratic formula: (ii) x^(2)+7x+12=0

The value of determinant |(x,x+y,x+2y),(x+2y,x,x+y),(x+y,x+2y,x)| is

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

    Text Solution

    |

  2. Find the equation of the line joining A( 1,3) and B (0,0) using det...

    Text Solution

    |

  3. Using properties of determinants, prove the following: |xx+y x+2y\...

    Text Solution

    |

  4. Using properties of determinants, prove the following: |alphabetag...

    Text Solution

    |

  5. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

    Text Solution

    |

  6. [[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3

    Text Solution

    |

  7. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

    Text Solution

    |

  8. Prove 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

    |

  9. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

    Text Solution

    |

  10. Using the Properties of determinants, prove that following: {:|(-a^2...

    Text Solution

    |

  11. Using the Properties of determinants, prove the following: {:|(1,1...

    Text Solution

    |

  12. If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...

    Text Solution

    |

  13. Using properties of determinants, solve the following for x: |x-2 ...

    Text Solution

    |

  14. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

    Text Solution

    |

  15. Using Properties of determinants, solve the following for x: {:|(x+a...

    Text Solution

    |

  16. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

    Text Solution

    |

  17. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

    Text Solution

    |

  18. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^2

    Text Solution

    |

  19. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

    Text Solution

    |

  20. Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(...

    Text Solution

    |