<p>The coefficient of \(x^3\) in the cubic polynomial, \(\mathrm{f}(x)\), is \(3\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Given that the roots of the equation, \(\mathrm{f}(x)=0\), are \(-5\), \(2p\) and \(p\), find an expression for&nbsp;\(\mathrm{f}(x)\) in terms of \(p\).</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Given also that the coefficient of \(x\) is \(-21\), find the possible value(s) of \(p\).</span><span class="inline-marks">[3]</span></div></li></ol>

The coefficient of \(x^3\) in the cubic polynomial, \(\mathrm{f}(x)\), is \(3\).

Given that the roots of the equation, \(\mathrm{f}(x)=0\), are \(-5\), \(2p\) and \(p\), find an expression for \(\mathrm{f}(x)\) in terms of \(p\).

Given also that the coefficient of \(x\) is \(-21\), find the possible value(s) of \(p\).

Polynomials, Cubic Equations and Partial Fractions - Remainder and Factor Theorems

Question 273ba6a6

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