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

If the equation `(a^2+b^2)x^2-2(a c+b d)x+c^2+d^2=0` has equal roots, then
(a)`a b=c d` (b) `a d=b c` (c) `a d=sqrt(b c)` (d)`a b=sqrt(c d)`

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 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

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

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!=b c .

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

If a x^2+b x+c=0 has equal roots, then c= (a) b/(2a) (b) b/(2a) (c) (-b^2)/(4a) (d) (b^2)/(4a)

The value of c for which the equation a x^2+2b x+c=0 has equal roots is (a) (b^2)/a (b) (b^2)/(4a) (c) (a^2)/b (d) (a^2)/(4b)

If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roots, then p can be (sqrt(a)-sqrt(b))^2 b. (sqrt(a)+sqrt(b))^2 c. a+b d. a-b

If the solution set of the inequaiton (x+4)(x-1)(x-3)(x+1)<0 is x in (a , b)uu(c , d) then (a) a+b+c+d=1 (b) a+b+c+d=2 (c) a b c d=12 (d) a b+c d=7

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

RD SHARMA ENGLISH-QUADRATIC EQUATIONS-All Questions
  1. The positive value of k for which the equation x^2+k x+64=0 and x^2-8x...

    Text Solution

    |

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

    Text Solution

    |

  3. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. The sum of the squares of three consecutive natural numbers is 149. ...

    Text Solution

    |

  16. The sum of two numbers is 9. The sum of their reciprocals is ½. Find ...

    Text Solution

    |

  17. A two digit number is such that the product of its digits is 18. When ...

    Text Solution

    |

  18. The denominator of a fraction is one more than twice the numerator. If...

    Text Solution

    |

  19. A two digit number is four times the sum and three times the product o...

    Text Solution

    |

  20. To fill swimming pool two pipes are to be used. If the pipe of larger ...

    Text Solution

    |