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Difference of roots and difference of cubes

Difference of roots and difference of cubes

IB Year 6 | Grade 12

The roots of the equation \(2x^2-3x-7=0\) are \(\alpha\) and \(\beta\). Without solving the equation, find the value of each of the following. You may assume that \(\alpha>\beta\).

  1. \(\alpha-\beta\)
  2. \(\alpha^3-\beta^3\)

Solution:

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Answer:(a) \(\frac{\sqrt{65}}{2}\) (b) \(\frac{23\sqrt{65}}{8}\)

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