Multiple choice

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2-12x+35 = 0$, then find the value of $2\begin{pmatrix}\dfrac{\alpha}{\beta}+\dfrac{\beta}{\alpha}\end{pmatrix} :$

  1. $\dfrac{74}{35}$
  2. $\dfrac{148}{35}$
  3. $\dfrac{12}{35}$
  4. $\dfrac{34}{35}$
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B Correct answer
Explanation

For x^2 - 12x + 35 = 0, alpha + beta = 12 and alpha * beta = 35. The expression is 2 * ((alpha^2 + beta^2) / (alpha * beta)). Since alpha^2 + beta^2 = (alpha + beta)^2 - 2*alpha*beta = 144 - 70 = 74. The value is 2 * (74 / 35) = 148 / 35.

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