Home
Class 11
MATHS
If a,b,c are in G.P., then the equations...

If a,b,c are in G.P., then the equations `ax^2+2bx+c =0` and `dx^2+2ex+f =0` have a common root if d/a,e/b,f/c are in

A

AP

B

GP

C

HP

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos
  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

If a, b, c are in G.P. and the equation ax^(2) + 2bx + c = 0 and dx^(2) + 2ex + f = 0 have a common root, then show that (d)/(a), (e)/(b), (f)/(c ) are in A.P.

If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 have a common root, then show that d/p, e/q, f/r are in AP.

Find the condition if equations ax^2+bx+c =0 and x^2+2x+3 =0 have a common root. (a,b,cinR)

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, then a+b+c =

If a ,b ,c , are in A.P then the roots of the equation ax^(2)-2bx+c=0

a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0 and dx^ 2 +2ex+f=0 have a common root, then prove that d/a,e/b,f/c are in A.P.

If the equations x^2 + 2x + 3 = 0 and ax^2 + bx + + c = 0 have common root, then a : b : c is _____

IF a,b,c are in G.P prove that the roots of the equation ax^2+2bx+c=0 are equal.

If the equation x^2+2x+3=0 and ax^2+bx+c=0 , a, b, c in R, have a common root, then a:b:c is

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where a,b,c are non zero real number...

    Text Solution

    |

  2. If a,b,c in AP and x=sum(n=0)^inftya^n,y=sum(n-0)^inftyb^n,z=sum(n-0)^...

    Text Solution

    |

  3. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

    Text Solution

    |

  4. If the product of n positive number is unity, then their sum is

    Text Solution

    |

  5. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

  6. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

    Text Solution

    |

  7. If a1,a2,.....an are positive real number whose product is a fixed num...

    Text Solution

    |

  8. The greatest value x^2y^3 is, where xgt0 and ygt0 are connected by the...

    Text Solution

    |

  9. Let S=8/5+16/65+......128/(2^18+1) then

    Text Solution

    |

  10. The sum of the infinite terms of the series 5/(3^2. 7^2)+9/(7^2. 11^2)...

    Text Solution

    |

  11. The sum to infinity of the series 1+2/3+6/3^2+10/3^3+14/3^4+....

    Text Solution

    |

  12. The sum to n terms of the series 1+2(1+1/n)+3(1+1/n)^2+....... is give...

    Text Solution

    |

  13. For absx lt1 the value of 1+3x+6x^2+10x^3+.....t o infty is

    Text Solution

    |

  14. If pth, qth, and rth term of an AP are equal to corresponding terms of...

    Text Solution

    |

  15. If a,b,c are positive real number, then the least value of (a+b+c)(1/a...

    Text Solution

    |

  16. An infinite GP has first term x and sum 5, then x belongs to

    Text Solution

    |

  17. 2^(1/4),2^(2/8),2^(3/16),2^(4/32)......infty is equal to

    Text Solution

    |

  18. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

    Text Solution

    |

  19. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all x,yin N such ...

    Text Solution

    |

  20. Sum of n terms of the series 8+88+888+....equals

    Text Solution

    |