Q54 / 160 · TS EAMCET 2004 · Mathematics

The set of all solutions of the inequation $x^2-2 x+5 \leq 0$ in $R$ is

  • A
    $R-(-\infty,-5)$
  • B
    $R-(5,\infty)$
  • Correct answer
    C
    $\phi$
  • D
    $R-(-\infty,-4)$

Solution

Given inequation is $x^2-2 x+5 \leq 0$. $\therefore$ Roots are $$ x=\frac{+2 \pm \sqrt{4-20}}{2}=\frac{2 \pm 4 i}{2} $$ $\therefore$ Roots are imaginary, therefore no real solutions exist.

Hence, the correct answer is option: 'C'.

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