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. For what value of k, (x + y + z)^2 + k(x^2 +y^2 + z^2) can be resolve...

    Text Solution

    |

  2. If (x-1)^(2) is a factor of ax^(3) +bx^(2) +c then roots of the equa...

    Text Solution

    |

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

    Text Solution

    |

  4. If |x|+|x-1|=3 then x= .

    Text Solution

    |

  5. The solution-set of the equation log5log2(sqrt(4x+2)+2sqrt2)=0 is .

    Text Solution

    |

  6. Fill in the blanks If x<0,y<0,x+y+(x//y)=(1//2)a n d(x+y)(x//y)=-(1//2...

    Text Solution

    |

  7. The number of real solutions of the equation |x^2|-3|x|+2=0 is .

    Text Solution

    |

  8. If x-=2+^(2//3)"then the value"(x^(3)-6x^(2)+6x)is

    Text Solution

    |

  9. The AM of the roots of x^2-12x+3=0 is .

    Text Solution

    |

  10. The GM of the roots of x^3-6x^2+11x-6=0 is .

    Text Solution

    |

  11. The quadratic equation whose roots are twice the roots of x^2-3x+3=0 i...

    Text Solution

    |

  12. The quadratic equation whose roots are 2 more than the roots of ax^2+b...

    Text Solution

    |

  13. If alpha,beta are roots of ax^2+2bx+c=0 then sqrt(alpha/beta)+sqrt(bet...

    Text Solution

    |

  14. if 2 = I sqrt3 be a root of the equation x^(2) + px + q =0, where p ...

    Text Solution

    |

  15. The value of sqrt(2+sqrt(2+sqrt(2+......oo is .

    Text Solution

    |

  16. If the roots of x(3-x^2)+2x^2=0 are alpha,beta,gamma then the value of...

    Text Solution

    |

  17. If the roots of 4-3x+5x^2+x^3=0 are alpha,beta,gamma then the value of...

    Text Solution

    |

  18. The equation x^2+2(gamma+1)x+a(a-4)=0 has negative roots only if gamma...

    Text Solution

    |

  19. The solution-set of x^4-1>0,x in R is .

    Text Solution

    |

  20. If x^(2)+ax+b=0 and x^(2)+bx+a=0,(a ne b) have a common root, then a+b...

    Text Solution

    |