Home
Class 12
MATHS
If a,b,c are in GP, show that the equati...

If `a,b,c` are in GP, show that the equations `ax^(2)+2bx+c=0` and `dx^(2)+2ex+f=0` have a common root if `a/d,b/e,c/f` are in HP

A

A.P.

B

G.P.

C

H.P.

D

ab = cd

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -C) (objective Type Questions ( more thena one options are correct )|35 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -D) Linked comprehension Type Questions|14 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

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 a ,b ,a n dc are in G.P., then the equations a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root if d/c , e/b ,f/c are in a. A.P. b. G.P. c. H.P. d. none of these

If d,e,f are G.P. and the two quadratic equations ax^(2)+2bx+c=0anddx^(2)+2ex+f=0 have a common root, then

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

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

If a,b,c in R and the equation ax^2+bx+c = 0 and x^2+ x+ 1=0 have a common root, then

If a,b,c, in R and equations ax^(2) + bx + c =0 and x^(2) + 2x + 9 = 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 positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. If the minimum value ofx^2+2x+3 is m and maximum value of -x^2+4x+6 is...

    Text Solution

    |

  2. for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

    Text Solution

    |

  3. If one root of equation (l-m) x^2 + lx + 1 = 0 be double of the other ...

    Text Solution

    |

  4. if p,q,r are real numbers satisfying the condition p + q +r =0 , then ...

    Text Solution

    |

  5. The roots of the equation x^(3) -2x^(2) -x +2 =0 are

    Text Solution

    |

  6. IF alpha , beta are the roots of the equation x^2+2ax +b=0 , the...

    Text Solution

    |

  7. The set of all values of ' a ' for which the quadratic equation 3x^2+2...

    Text Solution

    |

  8. Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,the...

    Text Solution

    |

  9. If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2...

    Text Solution

    |

  10. If a(1),a(2),a(3),a(4),,……, a(n-1),a(n) " are distinct non-zero real...

    Text Solution

    |

  11. If coefficients of the equation ax^2 + bx + c = 0 , a!=0 are real and...

    Text Solution

    |

  12. If the sum of the roots of the quadratic equaion ax^2+ bx +c =0 is equ...

    Text Solution

    |

  13. The number of irrational roots of the equation (x-1) (x-2) (3x-2) (...

    Text Solution

    |

  14. If alpha in (0,pi/2),t h e nsqrt(x^2+x)+(tan^2alpha)/(sqrt(x^2+x)) is ...

    Text Solution

    |

  15. If a,b are real, then the roots of the quadratic equation (a-b)x^(2)-5...

    Text Solution

    |

  16. If alpha, beta are the roots of the equation ax^(2) -bx +c=0 then eq...

    Text Solution

    |

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

    Text Solution

    |

  18. Find the least integral value of k for which the equation x^(2)-2(k+2)...

    Text Solution

    |

  19. The roots x(1) and x(2) of the equation x^(2) +px +12=0 are such tha...

    Text Solution

    |

  20. If a lt b lt c lt d, then for any real non-zero lambda, the quadratic...

    Text Solution

    |