Home
Class 12
MATHS
a,b,c are positive real numbers forming ...

a,b,c are positive real numbers forming a. G.P. If `ax ^(2) + 2 bx + c=0 and dx ^(2) + 2 ex + f =0` have a common root, pairs (a,b) of real numbers such that `d/a,e/b,f/c` are in arithmetic progression.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -1 PART -II RMO|1 Videos
  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)|15 Videos
  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise SELF PRACTICE PROBLEMS |23 Videos
  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos
  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

Similar Questions

Explore conceptually related problems

a,b,c are positive real numbers forming a G.P. ILf 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.

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

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

a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If ax^(2)+bx+c=0 and bx^(2)+cx+a=0 have a common root, prove that a+b+c=0 or a=b=c .

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

If a, b, c are in GP , 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

If ax^(2)+bx+c=0andbx^(2)+cx+a=0 have a common root then the relation between a,b,c is

If ax^2 + bx + c = 0 and bx^2 + cx+a= 0 have a common root and a!=0 then (a^3+b^3+c^3)/(abc) is

RESONANCE ENGLISH-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. The sum of three numbers in A.P. is 27, and their product is 504, find...

    Text Solution

    |

  2. Three friends whose ages form a G.P. divide a certain sum of money in ...

    Text Solution

    |

  3. The roots of the equation x ^(5) - 40 x ^(4) + ax ^(3) + bx ^(2) + cx ...

    Text Solution

    |

  4. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

    Text Solution

    |

  5. If a, b, c are in A.P. and if (b-c)x^(2)++(c-a)x+a-b=0and2(c+a)x^(2)+(...

    Text Solution

    |

  6. Along a road lies an odd number of stones placed at intervals of 10 m....

    Text Solution

    |

  7. a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=...

    Text Solution

    |

  8. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

    Text Solution

    |

  9. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  10. If n is any positive integer, then find the number whose square is und...

    Text Solution

    |

  11. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6)...

    Text Solution

    |

  12. If S (1), S (2) , S (3)……., S (2n) are the sums of infinite geometric ...

    Text Solution

    |

  13. Find the nth terms and the sum to n term of the series : 1^(2)+(1^(2...

    Text Solution

    |

  14. Let a (j) = (7)/(4) ((2)/(3)) ^( j -1), j in N. lf b (j) = a (j) ^(2...

    Text Solution

    |

  15. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

    Text Solution

    |

  16. As show in the figure , the five circles are tangent to one another co...

    Text Solution

    |

  17. The arithmaeic mean of the nine numbers in the given set {9,99,999,….....

    Text Solution

    |

  18. Let a sequence whose n^(th) term is {a(n)} be defined as a(1) = 1/2 ...

    Text Solution

    |

  19. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

    Text Solution

    |

  20. Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are th...

    Text Solution

    |