Now You Try

<p>State the zeros of the following functions.</p><p> <code class='latex inline'>y=5(2x+3)(4x-5)(x+7)</code></p>

<p>Find the cubic function that has the following zeros.</p><p>Zeros: <code class='latex inline'>-3, 0, 2</code></p>

<p>State the zeros of the following functions.</p><p> <code class='latex inline'>f(x)=x(x-2)^2(x+5)</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>y=2x(x-1)(x+2)(x-2)</code></p>

<p>Find the zeros of the function <code class='latex inline'>f(x) = 3x - 1+ \frac{1}{x + 1}</code></p>

<p>The distance of a ship from its harbour is modelled by the function <code class='latex inline'>d(t)=-3t^3+3t^2+18t</code>, where <code class='latex inline'>t</code> is the time elapsed in hours since departure from the harbour.</p><p>When does the ship return to the harbour?</p><p>There is another zero of <code class='latex inline'>d(t)</code>. What is it, and why is it not relevant to the problem?</p>

<p>Locate the <code class='latex inline'>x</code>-intercepts of the graph of the function.</p><p><code class='latex inline'>
\displaystyle
f(x) = -4x^2 + 25x - 21
</code></p>

<p>The distance of a ship from its harbour is modelled by the function <code class='latex inline'>d(t)=-3t^3+3t^2+18t</code>, where <code class='latex inline'>t</code> is the time elapsed in hours since departure from the harbour.</p><p>Estimate the time that the ship begins its return trip back
to the harbour.</p>

<p>During a normal 5 s respiratory cycle in which a person inhales and
then exhales, the volume of air in a person's lungs can be modelled by <code class='latex inline'>V(t)=0.027t^3-0.27t^2+0.675t</code>, where the volume, <code class='latex inline'>V</code>, is measured in litres at <code class='latex inline'>t</code> seconds.</p><p>What restriction(s) must be placed on <code class='latex inline'>t</code>?</p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>f(x)=-3x^3(2x+4)(x^2-25)</code></p>

<p>Solve.</p><p><code class='latex inline'>x^3+12x^2+21x-4=x^4-2x^3-12x^2-4</code></p>

<p>Solve each of the following equations by factoring.</p><p><code class='latex inline'>2x^4=48x^2</code></p>

<p>Solve each of the following equations by factoring.</p><p> <code class='latex inline'>3x^3=26x</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>y=(x+5)(x^2-4x-12)</code></p>

<p>Determine the break-even quantities for each profit function, where <code class='latex inline'>x</code> is the number sold, in thousands.</p><p><code class='latex inline'>
\displaystyle
P(x) = -2x^2 +18x - 40
</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>f(x)=(x^2+36)(8x-16)</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>y=(x+6)^3(2x-5)</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>y=-5x(x^2-9)</code></p>

<p>State the zeros of the following functions.</p><p> <code class='latex inline'>f(x)=(x+1)(x^2+2x+1)</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>f(x)=(x^3+1)(x-17)</code></p>

<p>Solve each of the following equations by factoring.</p><p><code class='latex inline'>4x^4=24x^2+108</code></p>

<p>During a normal <code class='latex inline'>5</code>s respiratory cycle in which a person inhales and
then exhales, the volume of air in a person's lungs can be modelled by <code class='latex inline'>V(t)=0.027t^3-0.27t^2+0.675t</code>, where the volume, <code class='latex inline'>V</code>, is measured in litres at <code class='latex inline'>t</code> seconds.</p><p>If asked, "How many seconds have passed if the volume of air in a person's lungs is 0.25 L?" would you answer this question algebraically or by using graphing technology? Justify your decision. </p><p>Solve the problem.</p>

<p>The distance of a ship from its harbour is modelled by the function <code class='latex inline'>d(t)=-3t^3+3t^2+18t</code>, where <code class='latex inline'>t</code> is the time elapsed in hours since departure from the harbour.</p><p>Draw a sketch of the function where <code class='latex inline'>0\leq t\leq3</code>.</p>

<p>Solve each of the following equations by factoring.</p><p> <code class='latex inline'>3x^4+5x^3-12x^2-20x=0</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>f(x)=(x^2-x-12)(3x)</code></p>

<p>Both equations <code class='latex inline'>x^3 - 12x + 16 = 0</code> and <code class='latex inline'>x^3 - 12x - 16 = 0</code> have double real root, and one other real root that is different from the double root.</p><p>For </p><p><code class='latex inline'>\begin{cases} x^3 - 12x + 20 = 0\\ x^3 - 12 x + 10 = 0 \\ x^3 - 12 x - 20 = 0 \end{cases}</code></p><p>Determine the values of <code class='latex inline'>k</code> for which the equation <code class='latex inline'>x^3 - 12x + k = 0</code> has:</p>
<ul>
<li>three different real roots</li>
<li>only one real roots</li>
</ul>

<p>Solve each of the following equations by factoring.</p><p><code class='latex inline'>10x^3+26x^2-12x=0</code></p>

<p>Solve each of the following equations by factoring.</p><p><code class='latex inline'>2x^3+162=0</code></p>

<p>Locate the <code class='latex inline'>x</code>-intercepts of the graph of each function.</p><p><code class='latex inline'>
\displaystyle
f(x) = 3x^2 - 7x - 2
</code></p>

<p>State the zeros of the following functions.</p><p><code class='latex inline'>y=2(x-3)^2(x+5)(x-4)</code></p>