<ol class="abc-list"><li><div class="list-item-paragraph">Consider the equation \(4x^2 + kx +1 = 0\). For what values of \(k\) does this equation have two <strong>equal</strong> roots?</div></li></ol>
<p>Let&nbsp;\(f\) be the function \(f(\theta) = 2\cos{2\theta} + 4\cos{\theta} + 3\), for&nbsp;\( -360^{\circ} \leq \theta \leq 360^{\circ}\).</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Show that this function may be written as&nbsp;\(f(\theta) = 4\cos^2{\theta} + 4\cos{\theta} + 1\).</div></li><li><div class="list-item-paragraph">Consider the equation \(f(\theta) = 0\), for&nbsp;\( -360^{\circ} \leq \theta \leq 360^{\circ}\).</div><ol class="i-list"><li><div class="list-item-paragraph">How many distinct values of \(\cos{\theta}\) satisfy this equation?</div></li><li><div class="list-item-paragraph">Find all values of \(\theta\) which satisfy this equation.</div></li></ol></li><li><div class="list-item-paragraph">Given that&nbsp;\(f(\theta) = c\)  is satisfied by only three values of \(\theta\), find the value of \(c\).</div></li></ol>

Consider the equation \(4x^2 + kx +1 = 0\). For what values of \(k\) does this equation have two **equal** roots?

Let \(f\) be the function \(f(\theta) = 2\cos{2\theta} + 4\cos{\theta} + 3\), for \( -360^{\circ} \leq \theta \leq 360^{\circ}\).

Show that this function may be written as \(f(\theta) = 4\cos^2{\theta} + 4\cos{\theta} + 1\).

Consider the equation \(f(\theta) = 0\), for \( -360^{\circ} \leq \theta \leq 360^{\circ}\).

Given that \(f(\theta) = c\)  is satisfied by only three values of \(\theta\), find the value of \(c\).

Trigonometric Equations and Identities

International Baccalaureate Standard Level Mathematics