$\alpha ,\;\beta $ are the roots of the equation ${x^2} - 3x + a = 0$ and $\gamma ,\;\delta $ are the roots of the equation ${x^2} - 12x + b = 0$. If $\alpha ,\;\beta ,\;\gamma ,\;\delta $ form an increasing $G.P.$, then $(a,\;b) = $

  • A

    $(3, 12)$

  • B

    $(12, 3)$

  • C

    $(2, 32)$

  • D

    $(4, 16)$

Similar Questions

For a sequence $ < {a_n} > ,\;{a_1} = 2$ and $\frac{{{a_{n + 1}}}}{{{a_n}}} = \frac{1}{3}$. Then $\sum\limits_{r = 1}^{20} {{a_r}} $ is

Let $b_1, b_2,......, b_n$ be a geometric sequence such that $b_1 + b_2 = 1$ and $\sum\limits_{k = 1}^\infty  {{b_k} = 2} $ Given that $b_2 < 0$ , then the value of $b_1$ is 

The greatest integer less than or equal to the sum of first $100$ terms of the sequence $\frac{1}{3}, \frac{5}{9}, \frac{19}{27}, \frac{65}{81}, \ldots \ldots$ is equal to

  • [JEE MAIN 2022]

The $G.M.$ of the numbers $3,\,{3^2},\,{3^3},....,\,{3^n}$ is

The sum of first three terms of a $G.P.$ is $\frac{13}{12}$ and their product is $-1$ Find the common ratio and the terms.