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 real value of a for which x^2+i(a-1)x+5=0 will have a pair of con...

    Text Solution

    |

  2. If a, b, c are positive then both roots of the equation ax^2 + bx+c=0

    Text Solution

    |

  3. The expression a^2x^2+bx+1 will be positive for all x in R if

    Text Solution

    |

  4. If x ,y ,a n dz are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2...

    Text Solution

    |

  5. The least value of ax^2+bx+c,(a>0) is

    Text Solution

    |

  6. If x be real, then the maximum value of 5+4x-4x^2 will be equal to

    Text Solution

    |

  7. If x^2+p x=1 is a factor of the expression a x^3+b x=c , then a^2-c^2=...

    Text Solution

    |

  8. If a+b+c=0, then, the equation 3ax^(2)+2bx+c=0 has , in the interval ...

    Text Solution

    |

  9. If the value of ax^2+bx+c is always an integer for integral values of ...

    Text Solution

    |

  10. If a gt 1 , then the roots of the equation (1-a)x^(2)+3ax-1=0 are

    Text Solution

    |

  11. Fill in the blank : If f(x) = x+1/x , x in R Then the set of possible ...

    Text Solution

    |

  12. Fill in the blank : If 1+ i is a root of the equation ix^2-3x+p = 0 wh...

    Text Solution

    |

  13. Equation cos 2x+7=a(2-sin x) can have a real solution for

    Text Solution

    |

  14. If alpha,beta be the roots of x^2 - x-1 = 0 and An = alpha^n +beta^n, ...

    Text Solution

    |

  15. For all lambda in R, The equation ax^2+ (b - lambda)x + (a-b-lambda)= ...

    Text Solution

    |

  16. Prove that (a^2 + b^2) x^2 - 2b(a+c)x + (b^2+ c^2) ge 0 for all x in R...

    Text Solution

    |

  17. Let f(x)= x^4- 3x^3 + 2x^2-3x+ a.If f(sqrt-1)= 0 and a in R then prove...

    Text Solution

    |

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

    Text Solution

    |

  19. Find all numbers p for each of which the least value of the quadratic ...

    Text Solution

    |

  20. Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in ...

    Text Solution

    |