<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Find the range of values of \(m\) such that&nbsp;\((m - 6)x^2 - 8x + m &gt; 0\) for all values of \(x\).<span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Given that the quadratic equation \(px^2 - 2(p - q)x - (r - p) = 0\) has equal roots, prove that&nbsp;\(p = \frac{q^2}{2q - r}\).<span class="inline-marks">[4]</span></div></li></ol>

Find the range of values of \(m\) such that \((m - 6)x^2 - 8x + m > 0\) for all values of \(x\).

Given that the quadratic equation \(px^2 - 2(p - q)x - (r - p) = 0\) has equal roots, prove that \(p = \frac{q^2}{2q - r}\).

Quadratic Equations and Inequalities

Quadratic Equations and Inequalities