If $x$ is real and $k = \frac{{{x^2} - x + 1}}{{{x^2} + x + 1}},$ then

  • A

    $\frac{1}{3} \le k \le 3$

  • B

    $k \ge 5$

  • C

    $k \le 0$

  • D

    None of these

Similar Questions

Suppose the quadratic polynomial $p(x)=a x^2+b x+c$ has positive coefficient $a, b, c$ such that $b-a=c-b$. If $p(x)=0$ has integer roots $\alpha$ and $\beta$ then what could be the possible value of $\alpha+\beta+\alpha \beta$ if $0 \leq \alpha+\beta+\alpha \beta \leq 8$

  • [KVPY 2016]

If $x$ is a solution of the equation, $\sqrt {2x + 1}  - \sqrt {2x - 1}  = 1, \left( {x \ge \frac{1}{2}} \right)$ , then $\sqrt {4{x^2} - 1} $ is equal to 

  • [JEE MAIN 2016]

Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?

$I$. It has at least one negative root.

$II$. It has at least one positive root.

$III$. Both its roots are real.

  • [KVPY 2013]

The number of ordered pairs $(x, y)$ of positive integers satisfying $2^x+3^y=5^{x y}$ is

  • [KVPY 2020]

The number of real solution of equation $(\frac{3}{2})^x =  -x^2 + 5x-10$ :-