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` are equal, prove that `a/b=c/d`.

Promotional Banner

Topper's Solved these Questions

  • PATHA BHAVAN

    UNITED BOOK HOUSE|Exercise EXERCISE|55 Videos

  • Pythagoras Theorem

    UNITED BOOK HOUSE|Exercise Exercise |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 be equal then prove that (a)/(b)=(c)/(d)

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 (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 .

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 .

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 equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

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

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)

UNITED BOOK HOUSE-PATRASAYER BAMIRA GURUDAS INSTITUTION, BANKURA-EXERCISE
  1. Two friends invested Rs 40,00 and Rs 50,00 respectively to stard a bu...

    Text Solution

    |

  2. Solve: 1/x-1/(x+b)=1/a-1/(a+b) (x!=0,-b).

    Text Solution

    |

  3. If the roots of the quadratic equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2...

    Text Solution

    |

  4. If (x+sqrt(x^2-1))/(x-sqrt(x^2-1))+(x-sqrt(x^2-1))/(x+sqrt(x^2-1))= 14...

    Text Solution

    |

  5. If 1/x-1/y alpha 1/(y-x), show that x alpha y.

    Text Solution

    |

  6. If ay - bx/c = cx - az/b = bz - cy/a, then prove that x/a = y/b = z/c.

    Text Solution

    |

  7. If x/(y+z)=y/(z+x)=z/(x+y) prove that the value of each ratio is eithe...

    Text Solution

    |

  8. State and prove Pythagoras theorem.

    Text Solution

    |

  9. Prove that opposite angles of a cyclic quadrilateral are supplementary

    Text Solution

    |

  10. O is any point inside a rectangle. Prove that OA^2+OC^2=OB^2+OD^2.

    Text Solution

    |

  11. ABCD is a cyclic quadrilaterla. Extended AB and DC intersect at P. Pr...

    Text Solution

    |

  12. Geometrically calculate the value of sqrt(23). (Only traces of constru...

    Text Solution

    |

  13. Draw a triangle whose one of the side is 7.2 cm and adjacent angles of...

    Text Solution

    |

  14. Sum of two angles is 135^@ and their difference is pi^c/12. Find the s...

    Text Solution

    |

  15. If costheta= x/sqrt(x^2+y^2) show that x sin theta = y cos theta.

    Text Solution

    |

  16. If sin 17^@ = x/y show that sec 17^@-sin 73^@ = x^2/(ysqrt(y^2-x^2).

    Text Solution

    |

  17. From a point on the roof of five storied building the angle of elevati...

    Text Solution

    |

  18. Mohit, standing in the midst of a field, observes a flying birds in hi...

    Text Solution

    |

  19. The curved surface of a solid metalic sphere is cut in such a way tha...

    Text Solution

    |

  20. A right circular cylindrical tank of 9 metre height is filled with wat...

    Text Solution

    |