If $\alpha $ and $\beta $ are the roots of the equation ${{x}^{2}}+2x-5=0$ where \(\alpha \be

Question

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. $\frac{1}{\alpha }+\frac{1}{\beta }$ ${{\alpha }^{2}}+{{\beta }^{2}}$ $\alpha -\beta $ ${{\alpha }^{3}}-{{\beta }^{3}}$ ${{\alpha }^{4}}+{{\beta }^{4}}$

Accepted Answer

(i) $\frac25$. (ii) $14$. (iii) $2\sqrt6$. (iv) $18\sqrt6$. (v) $146$.

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

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

Solution:

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