Home
Class 10
MATHS
If one root of the equation ax^(2)+bx+c=...

If one root of the equation `ax^(2)+bx+c=0` be double the another root of the eqaution, then prove that `2b^(2)=9ac.`

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 equation ax^2+bx+c=0(a!=0) be equal then

If the roots of the equation ax^(2)+bx+c=0(ane0) be equal, then

The roots of the equation ax^2+bx+c=0 are equal when-

If one root of the equation ax^2+bx+c=0 is square the other root, then prove that b^3+ac^2+a^2c= 3abc .

One root of the equation ax^2+bx+c=0(ane0) is zero when-

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) .

If the two roots of the equation ax^2 + bx + c = 0 are distinct and real then

If one root of the quadratic equation ax^2+bx+c=0 is equal to the n^th power of the other root then show that, (ac^n)^(1/(n+1))+(a^nc)^(1/(n+1))+b =0

If one root of the equation x^2+bx+8=0 be 4 and the roots of the equation x^2+bx+c=0 are equal , find the value of c.

If one root of the equation ax^2+bx+c=0 (a!=0) is twice the other, than show that 2b^2=9ac .

CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.5
  1. If one root of the equation ax^(2)+bx+c=0 be double the another root o...

    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

    |