If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} - 3x + 4}}{{{x^2} + 3x + 4}}$ will be

  • [IIT 1984]
  • A

    $2, 1$

  • B

    $5,\frac{1}{5}$

  • C

    $7,\frac{1}{7}$

  • D

    None of these

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If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$, then

  • [IIT 1980]

The sum of the solutions of the equation $\left| {\sqrt x  - 2} \right| + \sqrt x \left( {\sqrt x  - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

  • [JEE MAIN 2019]

The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by