2. Solved Papers
  3. JEE Main & Advanced

JEE Main & Advanced JEE Main Paper (Held on 08-4-2019 Afternoon)

  • question_answer
    If three distinct numbers a,b,c are in G.P. and the equations \[a{{x}^{2}}+2bx+c=0\]and \[d{{x}^{2}}+2ex+f=0\]have a common root, then which one of the following statements is correct?                                                                                                             [JEE Main 8-4-2019 Afternoon]

    A) d, e, ? are in A.P.

    B) \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\]a b c are in G.P.

    C) \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\]are in A.P.

    D) d, e, ? are in G.P.

    Correct Answer: C

    Solution :

    a, b, c in G.P. \[say\,a,\,ar,\,a{{r}^{2}}\] satisfies \[a{{x}^{2}}+2bx+c=0\]\[\Rightarrow \]\[x=-r\] \[x=-r\]is the common root, satisfies second equation \[d(-{{r}^{2}})+2e(-r)+f=0\] \[\Rightarrow \]\[d.\frac{c}{a}-\frac{2ce}{b}+f=0\]\[\Rightarrow \]\[\frac{d}{a}+\frac{f}{c}=\frac{2e}{b}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner