Home
Class 10
MATHS
If the roots of the quadratic equation (...

If the roots of the quadratic equation `(a^(2)+b^(2))x^(2)-2(ac+bd)x+(c^(2)+d^(2))=0` be equal then prove that `(a)/(b)=(c)/(d)`

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.1|29 Videos

  • QUADRATIC EQUATION IN ONE VARIABLE

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.2|26 Videos

  • PYTHAGORAS THEOREM

    CALCUTTA BOOK HOUSE|Exercise EXAMPLE 6|4 Videos

  • QUADRATIC SURDS

    CALCUTTA BOOK HOUSE|Exercise Exercise -3.2|28 Videos

Similar Questions

Explore conceptually related problems

If the roots of the quadratic equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 are equal, prove that a/b=c/d .

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

Prove that the quadratic equation (a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0 has no real roots when ad!=bc .

Prove that, if the roots of the equation (a^2+b^2)x^2+2(bc+ad)x+(c^2+d^2)=0 be real, then they are equal.

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If the roots of the quadratic equation a(b-c)x^2+b(c-a)+c(a-b)=0 be equal then prove that a,b,c are in Harmonic progression .

If the ratio of the roots of the quadratic equation ax^(2)+bx+c=0 be m:n, then prove that ((m+n)^2)/(mn)=(b^(2))/(ac)

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0 and 3b^(2)=16 ac then

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 be equal to the sum of their squares, then prove that 2ac=ab+b^(2) .

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.5
  1. If the roots of the quadratic equation (a^(2)+b^(2))x^(2)-2(ac+bd)x+(c...

    Text Solution

    |

  2. If the roots of the quadratic equation x^(2)-m(2x-5)-6=0 are equal, th...

    Text Solution

    |

  3. The roots of the equation x^(2)+x-6=0 are

    Text Solution

    |

  4. If the roots of the equation 4x^(2)-5x+2=0" are "(alpha^(2))/(beta)and...

    Text Solution

    |

  5. If the product of the roots of the quadratic equation x^(2)-5kx+3e^(lo...

    Text Solution

    |

  6. The quadratic equation one root of which is (2-sqrt3),"is "x^(2)-4x+1=...

    Text Solution

    |

  7. If the roote of the quadratic equation x^(2)-p(x-3)-5=0 are equal then...

    Text Solution

    |

  8. The product of the roots of the quadratic equation ax^(2)+cx+b=0 is .

    Text Solution

    |

  9. The sum of the roots of the quadratic equation (2-sqrt3)x^(2)+x+1=0 is...

    Text Solution

    |

  10. Find the quadartic equation whose one root is (3-sqrt2)

    Text Solution

    |

  11. Find m, given that the difference of the roots of the equation 2x^2-12...

    Text Solution

    |

  12. Find the quadartic equation whose sum of the roots is 2 and sum of the...

    Text Solution

    |

  13. For what values of a, the roots of the quadratic equation x^(2)-(3a-1)...

    Text Solution

    |

  14. Determine the nature of the roots of the qaudratic equation 3sqrt2x^(2...

    Text Solution

    |

  15. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

    Text Solution

    |

  16. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

    Text Solution

    |

  17. If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0, then...

    Text Solution

    |

  18. If alphaandbeta be the roots of quadratic equation ax^(2)+bx+c=0, then...

    Text Solution

    |

  19. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

    Text Solution

    |

  20. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

    Text Solution

    |

  21. Solve by applying Sreedhar Acharya's formula - (px-1)(qx+2)+r=0

    Text Solution

    |