Home
Class 10
MATHS
If the equation (1+m^2)x^2+2m c x+(c^2-a...

If the equation `(1+m^2)x^2+2m c x+(c^2-a^2)=0` has equal roots, prove that `c^2=a^2(1+m^2)dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|183 Videos
  • REAL NUMBERS

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

Similar Questions

Explore conceptually related problems

If the equation (1+m^(2))x^(2)+2mcx+c^(2)-a^(2)= 0 has equal roots, show that c^(2)=a^(2)(1+m^(2)) .

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

If the equation mx^(2)+mx+1=-4x^(2)-x has equal roots, then the values of m are

If the equation x^2-(2 + m)x + (m2-4m +4) = 0 has coincident roots, then

If the equation x^(2)-x+ m^(2) = 0 has no real roots then m can satisfy

If the equation (m+6)x^(2)+(m+6)x+2=0 has real and distinct roots, then

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

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

If the roots of the equation (c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0 are equal, prove that either a=0 or a^3+b^3+c^3=3a b c dot

Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no real root, if a d!=bc dot

RD SHARMA ENGLISH-QUADRATIC EQUATIONS-All Questions
  1. Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c...

    Text Solution

    |

  2. find the values of k so, that the equation (3k+1)x^2+2(k+1)x+1=0 has e...

    Text Solution

    |

  3. If the equation (1+m^2)x^2+2m c x+(c^2-a^2)=0 has equal roots, prove t...

    Text Solution

    |

  4. If -5 is a root of the quadratic equation 2x^2+p x-15=0 and the quadra...

    Text Solution

    |

  5. Find the values of p for whch the equadratic equation (2p+1)x^2-(7p+2...

    Text Solution

    |

  6. If a x^2+b x+c=0 has equal roots, then c= (a)b/(2a) (b) b/(2a) (c) ...

    Text Solution

    |

  7. The positive value of k for which the equation x^2+k x+64=0 and x^2-8x...

    Text Solution

    |

  8. The value of sqrt(6+sqrt(6+sqrt(6+))) ..........is (a) 4 (b) 3 (c) ...

    Text Solution

    |

  9. If the equation (a^2+b^2)x^2-2(a c+b d)x+c^2+d^2=0 has equal roots, th...

    Text Solution

    |

  10. A pole has to be erected at a point on the boundary of a circular park...

    Text Solution

    |

  11. If 1+sqrt(2) is a root of a quadratic equation with rational coefficie...

    Text Solution

    |

  12. Write the sum of real roots of the equation x^2+|x|-6=0

    Text Solution

    |

  13. If the equation x^2-a x+1=0 has two distinct roots, then (a)|a|=2 (b...

    Text Solution

    |

  14. If one root of the equation 2x^2+b x+c=0 is three times the other, the...

    Text Solution

    |

  15. If one root of the equation 4x^2-2x+(lambda-4)=0 be the reciprocal of ...

    Text Solution

    |

  16. One fourth of a herd of camels was seen in the forest. Twice the squar...

    Text Solution

    |

  17. Out of a group of swans 7/2 times the square root of the number are p...

    Text Solution

    |

  18. The difference of the squares of two numbers is 45. The square of the ...

    Text Solution

    |

  19. If the sum of first n even natural numbers is 420, find the value of ...

    Text Solution

    |

  20. If 1 is the root of equation 3x^2+ax-2=0 and the quadratic equation a(...

    Text Solution

    |