The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is
The number of real solutions of the equation $x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0$ is
- [JEE MAIN 2024]
- A
$5$
- B
$3$
- C
$4$
- D
$1$
Similar Questions
In the equation ${x^3} + 3Hx + G = 0$, if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0,$ then the roots are
In the equation ${x^3} + 3Hx + G = 0$, if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0,$ then the roots are
If the set of all values of $a$, for which the equation $5 x ^3-15 x - a =0$ has three distinct real roots, is the interval $(\alpha, \beta)$, then $\beta-2 \alpha$ is equal to _____
- [JEE MAIN 2025]
The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be
The two roots of an equation ${x^3} - 9{x^2} + 14x + 24 = 0$ are in the ratio $3 : 2$. The roots will be
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are
The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are
- [IIT 1989]
If $\alpha, \beta $ and $\gamma$ are the roots of the equation $2{x^3} - 3{x^2} + 6x + 1 = 0$, then ${\alpha ^2} + {\beta ^2} + {\gamma ^2}$ is equal to
If $\alpha, \beta $ and $\gamma$ are the roots of the equation $2{x^3} - 3{x^2} + 6x + 1 = 0$, then ${\alpha ^2} + {\beta ^2} + {\gamma ^2}$ is equal to