<p>The roots of the quadratic equation $2{{x}^{2}}-x=10$ are $\alpha $ and $\beta $. Find the quadratic equations whose roots are </p>
<ol class="i-list"><li><div class="list-item-paragraph">${{\alpha }^{2}}$ and ${{\beta }^{2}}$</div></li><li><div class="list-item-paragraph">${{\alpha }^{3}}$ and ${{\beta }^{3}}$</div></li><li><div class="list-item-paragraph">${{\alpha }^{2}}-\frac{1}{\beta }\mathrm{ }$ and ${{\beta }^{2}}-\frac{1}{\alpha }$</div></li></ol>

The roots of the quadratic equation $2{{x}^{2}}-x=10$ are $\alpha $ and $\beta $. Find the quadratic equations whose roots are 

${{\alpha }^{2}}-\frac{1}{\beta }\mathrm{ }$ and ${{\beta }^{2}}-\frac{1}{\alpha }$

Quadratic Equations and Inequalities - Sum and Product of Roots

Question 172b1074