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<p>Consider the cubic equation \(x^3-12x^2+qx-8=0\), where&nbsp;\(q\) is real. In each of the following cases, its three roots are positive and distinct.</p>
<ol class="abc-list"><li data-list-item-id="compare-a" data-list-item-path="compare-a"><div class="list-item-paragraph">The roots form an arithmetic sequence. Find the roots and the value of \(q\).<span class="inline-marks">[5]</span></div></li><li data-list-item-id="compare-b" data-list-item-path="compare-b"><div class="list-item-paragraph">In a different case the roots form an increasing geometric sequence. Find the roots and the value of \(q\).<span class="inline-marks">[5]</span></div></li></ol>

Consider the cubic equation \(x^3-12x^2+qx-8=0\), where \(q\) is real. In each of the following cases, its three roots are positive and distinct.

The roots form an arithmetic sequence. Find the roots and the value of \(q\).

In a different case the roots form an increasing geometric sequence. Find the roots and the value of \(q\).

Cubic Expressions and Equations

Geometric Progression

Arithmetic Progression

Sum and Product of Polynomial Roots

Two sequence patterns for roots of a cubic

Polynomials, Cubic Equations and Partial Fractions

Sequence and Series

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