Multiple choice

If $\dfrac {1}{\alpha}$ is a root of the equation $2x^{2}-5x+7=0$, then the value of $7\alpha^{2}-5\alpha$ is

  1. $-2$
  2. $2$
  3. $5$
  4. $-5$
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A Correct answer
Explanation

If 1/alpha is a root, then 2(1/alpha)^2 - 5(1/alpha) + 7 = 0. Multiplying by alpha^2 gives 2 - 5alpha + 7alpha^2 = 0. Rearranging, 7alpha^2 - 5alpha = -2.

AI explanation

Substitute 1 divided by alpha into the equation to get 2 divided by alpha squared minus 5 divided by alpha plus 7 equals 0. Multiplying the entire equation by alpha squared yields 2 minus 5 alpha plus 7 alpha squared equals 0. Rearranging this result gives 7 alpha squared minus 5 alpha equals negative 2.

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