Multiple choice

Find the roots of the following quadratic equation by using the quadratic formula $\displaystyle x + \frac{1}{x} = 3, x \neq 0$

  1. $\displaystyle \frac{3 \pm \sqrt {13}}{2}$
  2. $\displaystyle \frac{3 \pm \sqrt 5}{2}$
  3. $\displaystyle \frac{-3 + \sqrt 5}{2}$
  4. $\displaystyle \frac{-3 \pm \sqrt {13}}{2}$
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B Correct answer
Explanation

Given x + 1/x = 3, multiplying by x gives x^2 - 3x + 1 = 0. Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a, we get x = (3 +/- sqrt(9 - 4)) / 2 = (3 +/- sqrt(5)) / 2.

AI explanation

Multiply the equation by x to get the quadratic form x squared minus 3x plus 1 equals 0. Using the quadratic formula with a equal to 1, b equal to negative 3 and c equal to 1, the discriminant is 9 minus 4, which is 5. The roots are 3 plus or minus the square root of 5, all divided by 2.

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