Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$Fromk=\frac{x^2-x+1}{x^2+x+1}$

We have $x^2$(k – 1) + x(k + 1) + k – 1 = 0

As given, x is real $\Rightarrow$ (k + 1) – 4$(k–1{)}^2$ ≥ 0

$\Rightarrow 3k^2$ – 10k + 3 ≥ 0

Which is possible only when the value of k

lies between the roots of the equation $3k^2$ – 10k + 3 = 0

That is, when $\frac{1}{3}$ ≤ k ≤ 3 {Since roots are $\frac{1}{3}$ and 3}