If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$ is
If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$ is
- A
$0$
- B
$20$
- C
$21$
- D
$23$
Similar Questions
If in the equation $a{x^2} + bx + c = 0,$ the sum of roots is equal to sum of square of their reciprocals, then $\frac{c}{a},\frac{a}{b},\frac{b}{c}$ are in
If in the equation $a{x^2} + bx + c = 0,$ the sum of roots is equal to sum of square of their reciprocals, then $\frac{c}{a},\frac{a}{b},\frac{b}{c}$ are in
The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $.....$
The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $.....$
- [JEE MAIN 2021]
The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$, the number of terms is
The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$, the number of terms is
The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots,$ $b_{ m }$ is $2$ more than the common difference of $A.P.$ $a _{1}, a _{2}, \ldots, a _{ n } .$ If $a _{40}=-159, a _{100}=-399$ and $b _{100}= a _{70},$ then $b _{1}$ is equal to
The common difference of the $A.P.$ $b_{1}, b_{2}, \ldots,$ $b_{ m }$ is $2$ more than the common difference of $A.P.$ $a _{1}, a _{2}, \ldots, a _{ n } .$ If $a _{40}=-159, a _{100}=-399$ and $b _{100}= a _{70},$ then $b _{1}$ is equal to
- [JEE MAIN 2020]
Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-
Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-