Question

If \(f(x) = \frac{x+2}{x^2-3x+1}\), then the values of \(x\) for which \(f(x)\) is not defined are

• A. \(x = \frac{3+\sqrt{5}}{2}, x = \frac{3-\sqrt{5}}{2}\)
• B. \(x = \frac{-3+\sqrt{5}}{2}, x = \frac{-3-\sqrt{5}}{2}\)
• C. \(x = \frac{3+\sqrt{3}}{2}, x = \frac{3-\sqrt{3}}{2}\)
• D. \(x = \frac{2+\sqrt{5}}{2}, x = \frac{2-\sqrt{5}}{2}\)

Hint:

The function is undefined where the denominator is zero.

Answer 1

The Correct Option is A

Step 1: Set denominator to zero
$x^2-3x+1=0$, discriminant $=9-4=5$.

Step 2: Roots
$x=(3\pm\sqrt5)/2$, which is option (A).

Final Answer:
The values are $\frac{3\pm\sqrt5}{2}$, option (A). \[ \boxed{\dfrac{3\pm\sqrt5}{2}} \]