Home
Class 12
MATHS
If one root of the equation ax^(2) + bx ...

If one root of the equation `ax^(2) + bx + c =0 ` is reciprocal of the one root of the equation
`a_(1)x^(2) + b_(1) + x + c_(1) = 0` , then :

A

`(a a_(1)-c c_(1))^(2)=(b c_(1)-b_(1) a)(b_(1) c-a_(1)`

B

`(a b_(1)-a_(1) b)^(2)=(b c_(1)-b_(1) c)(c a_(1)-c_(1)`

C

`(b c_(1)-b_(1) c)^(2)=(c a_(1)-a_(1) c)(a b_(1)-a_(1)` b)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|97 Videos
  • SETS,RELATIONS AND FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|285 Videos

Similar Questions

Explore conceptually related problems

Roots of the equation x^(2) -2x+ 1 =0 are :

If one root of the equation 6x^2 − 2 x + ( λ − 5 ) = 0 be the reciprocal of the other, then λ =

If one root of the equation 5 x^(2)+13 x+k=0 is reciprocal of other, then the value of k is

The roots of the quadratic equations ax^(2)+ bx =0 are:

The roots of the equation 12 x^2 + x - 1 = 0 is :

If the ratio of the roots of the equation a x^(2)+b x+c=0 is equal to the ratio of the roots of the equation x^(2)+x+1=0 , then a, b , c are in

Roots of equation x^(2)-2x+1=0 are:

In the equations ax^(2) + bx+ c =0 , if one roots is negative of the other then:

If the ratio of the roots of a_(1)x^(2) + b_(1) x + c_(1) = 0 be equal to the ratio of the roots of a_(2) x^(2) + b_(2)x + c_(2) = 0 , then (a_(1))/(a_(2)) , (b_(1))/(b_(2)) , (c_(1))/(c_(2)) are in :

if one of the root of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1,the other root is

HIMALAYA PUBLICATION-QUADRATIC EQUATIONS AND EXPRESSION-Question Bank
  1. If one root of x^(2)-x-k=0 is square of the other, then k=

    Text Solution

    |

  2. The value of p for which the difference between the roots of the equat...

    Text Solution

    |

  3. If one root of the equation ax^(2) + bx + c =0 is reciprocal of the o...

    Text Solution

    |

  4. If one root of the equation 5 x^(2)+13 x+k=0 is reciprocal of other, t...

    Text Solution

    |

  5. Let f(x)=a x^(2)+b x+c, a, b, in R, a neq 0 satisfying f(1)+f(2)=0 . T...

    Text Solution

    |

  6. If the roots of a x^(2)+b x+c=0(a ge 0) be each greater than unity, th...

    Text Solution

    |

  7. If a in Z and the equation (x-3)(x-a)+1=0 has integral roots, then the...

    Text Solution

    |

  8. If the equations x^(2)+b^(2)=1-2b x and x^(2)+a^(2)=1-2 a x have one a...

    Text Solution

    |

  9. The number of values of a such that x^(2)-11 x+a and x^(2)-14 x+2 a ha...

    Text Solution

    |

  10. If the equations a x^(2)+2 b x+c-0 and a x^(2)+2 c x+b=0, b ne c have ...

    Text Solution

    |

  11. If the equations x^(2)+a x+b=0 and x^(2)+b x+a=0(a ne b) have a common...

    Text Solution

    |

  12. If x^(2)-p x+q=0 has equal integral roots, then

    Text Solution

    |

  13. Find the condition that quadratic equations x^(2)+ax+b=0 and x^(2)+bx+...

    Text Solution

    |

  14. If both roots of the equation x^(2)-2 a x+a^(2)-1= 0 lie between -2 an...

    Text Solution

    |

  15. If alpha, beta are the roots of a x^(2)+b x+c=0 and A(n)=alpha^(n)+bet...

    Text Solution

    |

  16. If alpha, beta are the roots of x^(2)-a x+b=0 and A(n)='alpha'^(n)+bet...

    Text Solution

    |

  17. In the equation x^(2)+p x+q=0 the coefficient of x was incorrectly wri...

    Text Solution

    |

  18. If sum of the roots of the quadratic equation ax^(2) + bx+c = 0 is equ...

    Text Solution

    |

  19. If a, b, c are in A.P and (b-c) x^(2)+(c-a) x+(a-b)=0 and 2(c+a) x^(2)...

    Text Solution

    |

  20. If A,G and H are respectively A.M.,G.M. and H.M. of three positive num...

    Text Solution

    |