If $\alpha $ and $\beta $ are the roots of the equation $-2{{x}^{2}}+3x+2=0$ where \(\alpha \

Question

If $\alpha $ and $\beta $ are the roots of the equation $-2{{x}^{2}}+3x+2=0$ where $\alpha >\beta $, find the value for each of the following. ${{\alpha }^{2}}+{{\beta }^{2}}$ $\alpha -\beta $ ${{\alpha }^{2}}-{{\beta }^{2}}$ ${{\alpha }^{3}}+{{\beta }^{3}}$ $\frac{1}{{{\beta }^{2}}}+\frac{1}{{{\alpha }^{2}}}$

Accepted Answer

(i) $\dfrac{17}4$. (ii) $\dfrac52$. (iii) $\dfrac{15}4$. (iv) $\dfrac{63}8$. (v) $\dfrac{17}4$.

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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