Multiple choice

Form the quadratic equation in each of the following cases when the roots are $a$ and $\displaystyle \frac{1}{a}$.

  1. The required equation is $\displaystyle x^2 - \left(a - \frac{1}{a} \right) x + 1 = 0$
  2. The required equation is $\displaystyle x^2 - \left(a + \frac{1}{a} \right) x - 1 = 0$
  3. The required equation is $\displaystyle x^2 - \left(a - \frac{1}{a} \right) x - 1 = 0$

  4. None of these
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D Correct answer
AI explanation

Using the standard formula for forming a quadratic equation from its roots, the required equation is x squared minus the sum of the roots times x plus the product of the roots equals 0. Here, the sum of the roots is a plus 1 over a, and their product is 1. Therefore, the correct equation is x squared minus the quantity a plus 1 over a times x plus 1 equals 0, which is not listed among the given choices. The correct option is None of these.

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