Home
Class 12
MATHS
Theorem : A necessary and sufficient con...

Theorem : A necessary and sufficient condition for the quadratic equations `a_(1)x^(2)+b_(1)x+c_(1)=0" and "a_(2)x^(2)+b_(2)x+c_(2)=0` to have a common roots is
`(c_(1)a_(2)-c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))`

Text Solution

Verified by Experts

The correct Answer is:
Thus `alpha` is a common root of the given equations.
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Very Short Answer Questions|3 Videos

  • QUADRATIC EXPRESSIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Short Answer Questions|8 Videos

  • PROBABILITY

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise DAM SURE|13 Videos

  • QUESTION PAPER -2019

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Long Answer Type questions|7 Videos

Similar Questions

Explore conceptually related problems

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

If a_(1)Cos theta+b_(1) Sin theta+c_(1)=0 and a_(2) cos theta+ b_(2) sin theta +c_(2)= 0 then (b_(1)c_(2)-b_(2)c_(1))^(2)+(c_(1)a_(2)-c_(2)a_(1))^(2)=

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

If (a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)) are direction ratio of two lines such that (a_(1)^(2)+b_(1)^(2)+c_(1)^(2))(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))^(2)=0 then the two lines

If (a_(1), b_(1), c_(1)), (a_(2), b_(2), c_(2)) are d.r.'s of two perpendicular lines then

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) , then prove that a_(0)+a_(1)+a_(2)…..+a_(2n)=3^(n)

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)-a_(1)++a_(2)-a_(3)+……+a_(20)=4^(10)

If (1+3x-2x^(2))^(10)=a_(0)+a_(1)x+a_(2)x^(2).+…+a_(20)x^(20) then prove that a_(0)+a_(1)+a_(2)+……+a_(20)=2^(10)

If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))

If ax^(2) + by^(2) = 1, a_(1) x^(2) + b_(1)y^(2) = 1 , then show that the condition for orthogonality of above curves is (1)/(a)-(1)/(b)=(1)/(a_(1))-(1)/(b_(1))

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-QUADRATIC EXPRESSIONS-TEXTUAL EXERCISES
  1. Theorem : A necessary and sufficient condition for the quadratic equat...

    Text Solution

    |

  2. Find the roots of the following equations. x^(2)-7x+12=0

    Text Solution

    |

  3. Find the roots of the following equations. -x^(2)+x+2=0

    Text Solution

    |

  4. Find the roots of the following equations. 2x^(2)+3x+2=0

    Text Solution

    |

  5. Find the roots of the following equations. sqrt(3)x^(2)+10x-8sqrt(3)...

    Text Solution

    |

  6. Find the roots of the following equations. 6sqrt(5)x^(2)-9x-3sqrt(5)...

    Text Solution

    |

  7. Form quadratic equation whose roots are : 2,5

    Text Solution

    |

  8. Form quadratic equation whose roots are : (m)/(n), (n)/(m) (m ne 0, ...

    Text Solution

    |

  9. Form quadratic equation whose roots are : (p-q)/(p+q), (-p+q)/(p-q),...

    Text Solution

    |

  10. Form quadratic equation whose root 7 pm 2sqrt(5)

    Text Solution

    |

  11. Form quadratic equation whose roots are : -3 pm 5i

    Text Solution

    |

  12. Find the nature of the roots of the following equation, without findin...

    Text Solution

    |

  13. Find the nature of the roots of the following equation, without findin...

    Text Solution

    |

  14. Find the nature of the roots of the following equation, without findin...

    Text Solution

    |

  15. Find the nature of the roots of the following equation, without findin...

    Text Solution

    |

  16. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

    Text Solution

    |

  17. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

    Text Solution

    |

  18. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

    Text Solution

    |

  19. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

    Text Solution

    |

  20. If alpha, beta are the roots of the equation ax^(2)+bx+c=0, find the v...

    Text Solution

    |

  21. Find the values of m for which the following equations have equal root...

    Text Solution

    |