Home
Class 11
MATHS
If the roots of the equation (1)/(x+p) +...

If the roots of the equation `(1)/(x+p) +(1)/(x+q) =1/r` are equal in magnitude but opposite in sign, then the product of the roots is :

A

`(1)/(2)(a^(2) + b^(2))`

B

`-(1)/(2)(a^(2)+b^(2))`

C

`(1)/(2) ab`

D

`-(1)/(2) ab``

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|22 Videos

  • PROBABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|45 Videos

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation (1)/(x+a) + (1)/(x+b) = (1)/(c) are equal in magnitude but opposite in sign, then their product, is

If the roots of the equation 1/(x+p) + 1/(x+q) = 1/r are equal in magnitude but opposite in sign and its product is alpha

If two roots of the equation x^3 - px^2 + qx - r = 0 are equal in magnitude but opposite in sign, then:

If the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

If the roots of the equation 1/(x+p)+1/(x+q)=1/r are equal in magnitude and opposite in sign, then (A) p+q=r (B)p+q=2r (C) product of roots=- 1/2(p^2+q^2) (D) sum of roots=1

If the roots (1)/(x+k+1)+(2)/(x+k+2)=1 are equal in magnitude but opposite in sign, then k =

If roots of ax^2+bx+c=0 are equal in magnitude but opposite in sign, then

If the equation a/(x-a)+b/(x-b)=1 has two roots equal in magnitude and opposite in sign then the value of a+b is

If the equation a/(x-a)+b/(x-b)=1 has two roots equal in magnitude and opposite in sign then the value of a+b is

If two roots of x ^(3) -ax ^(2) + bx -c =0 are equal in magnitude but opposite in sign. Then:

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to ...

    Text Solution

    |

  2. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

    Text Solution

    |

  3. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

    Text Solution

    |

  4. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

    Text Solution

    |

  5. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

    Text Solution

    |

  6. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  7. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

  8. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

    Text Solution

    |

  9. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

    Text Solution

    |

  10. Fill in the blanks If the quadratic equations x^2+a x+b=0a n dx^2+b x+...

    Text Solution

    |

  11. Find the values of a for which the roots of the equation x^2+a^2=8x+6a...

    Text Solution

    |

  12. If the sum of the roots of the equation (a+1)x^2=(2a+3)x+(3a+4)=0 is -...

    Text Solution

    |

  13. If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciproca...

    Text Solution

    |

  14. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  15. Solve |x^2+4x+3|+2x+5=0.

    Text Solution

    |

  16. For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3...

    Text Solution

    |

  17. If 2+sqrt(3)i is a root of the equation x^2+p x+1=0 , then write the v...

    Text Solution

    |

  18. If tan alpha tan beta are the roots of the equation x^2 + px +q =0(p!...

    Text Solution

    |

  19. Root of the quadratic equation x^2+6x-2=0

    Text Solution

    |

  20. If sum of the roots of ax^(2)+bx+c=0 is equal to the sum of the square...

    Text Solution

    |