Home
Class 11
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

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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 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 x^2+2x+3=0 and ax^2+bx+c=0 have a common root then a:b:c is

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

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

OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

    Text Solution

    |

  16. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

    Text Solution

    |

  17. If the roots of the equation a x^2+2b x+c=0 and b x^2-2sqrt(a c) x+b=0...

    Text Solution

    |

  18. If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b,...

    Text Solution

    |

  19. if p and q are non zero constants, the equation x^2+px+q=0 has roots ...

    Text Solution

    |

  20. The equation x^((3)/4 (log2x)^2+log2 x -(5)/(4))=sqrt(2) has :

    Text Solution

    |