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Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

IP 3

If \(\alpha \) and \(\beta \) are the roots of the equation \(5{{x}^{2}}-4x-10=0\) where \(\alpha >\beta \), find the value for each of the following.

  1. \({{\alpha }^{2}}+{{\beta }^{2}}\)
  2. \(\alpha -\beta \)
  3. \({{\alpha }^{2}}-{{\beta }^{2}}\)
  4. \({{\alpha }^{4}}+{{\beta }^{4}}\)
  5. \(\frac{\alpha }{\beta }+\frac{\beta }{\alpha }\)

Solution:

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Answer:(i) \(\dfrac{116}{25}\). (ii) \(\dfrac{6\sqrt6}{5}\). (iii) \(\dfrac{24\sqrt6}{25}\). (iv) \(\dfrac{8456}{625}\). (v) \(-\dfrac{58}{25}\).

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