The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
- A
$1$
- B
$2$
- C
$3$
- D
$4$
Similar Questions
The number of positive integers $x$ satisfying the equation $\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}=\frac{13}{2}$ is.
The number of positive integers $x$ satisfying the equation $\frac{1}{x}+\frac{1}{x+1}+\frac{1}{x+2}=\frac{13}{2}$ is.
- [KVPY 2021]
If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
The number of integers $k$ for which the equation $x^3-27 x+k=0$ has at least two distinct integer roots is
The number of integers $k$ for which the equation $x^3-27 x+k=0$ has at least two distinct integer roots is
- [KVPY 2016]
Let $x, y, z$ be positive integers such that $HCF$ $(x, y, z)=1$ and $x^2+y^2=2 z^2$. Which of the following statements are true?
$I$. $4$ divides $x$ or $4$ divides $y$.
$II$. $3$ divides $x+y$ or $3$ divides $x-y$.
$III$. $5$ divides $z\left(x^2-y^2\right)$.
Let $x, y, z$ be positive integers such that $HCF$ $(x, y, z)=1$ and $x^2+y^2=2 z^2$. Which of the following statements are true?
$I$. $4$ divides $x$ or $4$ divides $y$.
$II$. $3$ divides $x+y$ or $3$ divides $x-y$.
$III$. $5$ divides $z\left(x^2-y^2\right)$.
- [KVPY 2017]
Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then
Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then