Home
Class 12
MATHS
If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3...

If `a_1x^3 + b_1x² + c_1x + d_1 = 0` and `a_2x^3 + b_2x^2+ c_2x + d_2 = 0` have a pair of repeated roots common, then prove that `|[3a_1,2b_1,c_1],[3a_2,2b_2,c_2],[a_2b_1-a_1b_2,c_1a_2-c_2a_1,d_1a_2-d_2a_1]|=0`

Promotional Banner

Topper's Solved these Questions

  • Ellipse and Hyberbola

    A DAS GUPTA|Exercise EXERCISE|65 Videos

  • Function

    A DAS GUPTA|Exercise Exercise|57 Videos

Similar Questions

Explore conceptually related problems

If a_(1)x^(2)+b_(1)x+c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 has a common root,then the common root is

Prove that |[1,a,a^2,a^3+bcd] , [1,b,b^2,b^3+cda] , [1,c,c^2,c^3+dab] , [1,d,d^2,d^3+abc]|=0

Three linear equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0,a_3x+b_3y+c_3z=0 are consistent if (A) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 (B) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=-1 (C) a_1b_1c_1+a_2b_2c_2+a_3b_3c_3=0 (D) none of these

If the roots of a_1x^(2)+b_1x+c_1=0 and alpha_1 , beta_1 and those of a_2x^(2)+b_2x+c_2=0 are alpha_2 , beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then :

A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

    Text Solution

    |

  2. if alpha is a real root of the quadratic equation ax^2+bx+c=0 and beta...

    Text Solution

    |

  3. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

    Text Solution

    |

  4. If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has at...

    Text Solution

    |

  5. For what values of a the following will be an identity in x ? (x^2-1)a...

    Text Solution

    |

  6. The number of integral triplets (a, b, c) such thet a+b cos 2x+c sin^(...

    Text Solution

    |

  7. Let k be the value of a for which the equation (a^2 + 4a + 3) x^2 + (a...

    Text Solution

    |

  8. Solve (x^2+2)^2+8x^2=6x(x^2+2)

    Text Solution

    |

  9. Solve (x+4)(x+7)(x+8)(x+11)+20=0.

    Text Solution

    |

  10. Solve sqrt(5x^2-6x+8)+sqrt(5x^2-6x-7)=1.

    Text Solution

    |

  11. Number of real solutions of sqrt(x)+sqrt(x-sqrt(1-x))=1 is

    Text Solution

    |

  12. Solve (x+3)^4+(x+2)^4+(x+1)^4 = 98.

    Text Solution

    |

  13. Solve for x : 2x^3+5x^2-2x+3 = 0.

    Text Solution

    |

  14. If the roots of the equation x^3-12 x^2+39 x-28=0 are in A.P. th...

    Text Solution

    |

  15. Obtain the real solutions for x,y. xy+3y^2-x+4y-7=0 and 2xy+y^2-2x-2y+...

    Text Solution

    |

  16. Solve for x,y,z. xy + x + y = 23 xz + z + x = 41 yz + y + z = 27.

    Text Solution

    |

  17. If a+b+c!=0, the system of equations (b+c)(y+z)-ax=b-c, (c+a)(z+x)-by=...

    Text Solution

    |

  18. Solve for x,y. x^2 + y(x+1) = 17 and y^2 + x(y+1) = 13

    Text Solution

    |

  19. 12^(5x-2)=(24sqrt3)^(3-x^2)

    Text Solution

    |

  20. Solve 32^((x+5)/(x-7))= 1/4 * 128^((x+17)/(x-3)).

    Text Solution

    |