<p>If $\alpha $ and $\beta $ are the roots of the equation ${{x}^{2}}+2x-5=0$ where $\alpha >\beta $, find the value for each of the following. </p>
<ol class="i-list"><li><div class="list-item-paragraph">$\frac{1}{\alpha }+\frac{1}{\beta }$</div></li><li><div class="list-item-paragraph">${{\alpha }^{2}}+{{\beta }^{2}}$</div></li><li><div class="list-item-paragraph">$\alpha -\beta $</div></li><li><div class="list-item-paragraph">${{\alpha }^{3}}-{{\beta }^{3}}$</div></li><li><div class="list-item-paragraph">${{\alpha }^{4}}+{{\beta }^{4}}$</div></li></ol>

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

Quadratic Equations and Inequalities - Sum and Product of Roots

Quadratic Equations and Inequalities - Sum and Product of Roots