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@@ -211,6 +211,9 @@ Functions</h2></td></tr>
<tr class="memitem:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#a8a48be4d7f14e34c5c92925bc1cbf3bb">power_of_two</a> (int n)</td></tr>
<tr class="memdesc:a8a48be4d7f14e34c5c92925bc1cbf3bb"><td class="mdescLeft">&#160;</td><td class="mdescRight">This function finds whether a number is power of 2 or not. <br /></td></tr>
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<tr class="memitem:aacb1411ef2029e81f249c21e17c96fdb"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">quadraticEquation</a> (long double a, long double b, long double c)</td></tr>
<tr class="memdesc:aacb1411ef2029e81f249c21e17c96fdb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Quadratic equation calculator. <br /></td></tr>
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<tr class="memitem:ae1ca505751f5a6d3977b86372cfe75ea"><td class="memItemLeft" align="right" valign="top">uint64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#ae1ca505751f5a6d3977b86372cfe75ea">binomialCoeffSum</a> (uint64_t n)</td></tr>
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@@ -1365,6 +1368,99 @@ template&lt;typename T &gt; </div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> length * width * height / 3;</div>
<div class="line"><span class="lineno"> 82</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aacb1411ef2029e81f249c21e17c96fdb">&#9670;&#160;</a></span>quadraticEquation()</h2>
<div class="memitem">
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<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt; math::quadraticEquation </td>
<td>(</td>
<td class="paramtype">long double&#160;</td>
<td class="paramname"><em>a</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">long double&#160;</td>
<td class="paramname"><em>b</em>, </td>
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<p>Quadratic equation calculator. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>quadratic coefficient. </td></tr>
<tr><td class="paramname">b</td><td>linear coefficient. </td></tr>
<tr><td class="paramname">c</td><td>constant </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>Array containing the roots of quadratic equation, incl. complex root. </dd></dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../df/dcd/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2math_2quadratic_equations_complex_numbers_8cpp-example.html#a1">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</a>.</dd>
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<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;quadratic coefficient cannot be 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> discriminant = b * b - 4 * a * c;</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; solutions{0, 0};</div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">if</span> (discriminant == 0) {</div>
<div class="line"><span class="lineno"> 64</span> solutions[0] = -b * 0.5 / a;</div>
<div class="line"><span class="lineno"> 65</span> solutions[1] = -b * 0.5 / a;</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> solutions;</div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> <span class="comment">// Complex root (discriminant &lt; 0)</span></div>
<div class="line"><span class="lineno"> 70</span> <span class="comment">// Note that the left term (-b / 2a) is always real. The imaginary part</span></div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// appears when b^2 - 4ac &lt; 0, so sqrt(b^2 - 4ac) has no real roots. So,</span></div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// the imaginary component is i * (+/-)sqrt(abs(b^2 - 4ac)) / 2a.</span></div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">if</span> (discriminant &gt; 0) {</div>
<div class="line"><span class="lineno"> 74</span> <span class="comment">// Since discriminant &gt; 0, there are only real roots. Therefore,</span></div>
<div class="line"><span class="lineno"> 75</span> <span class="comment">// imaginary component = 0.</span></div>
<div class="line"><span class="lineno"> 76</span> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 77</span> (-b - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"><span class="lineno"> 78</span> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 79</span> (-b + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> solutions;</div>
<div class="line"><span class="lineno"> 81</span> }</div>
<div class="line"><span class="lineno"> 82</span> <span class="comment">// Since b^2 - 4ac is &lt; 0, for faster computation, -discriminant is</span></div>
<div class="line"><span class="lineno"> 83</span> <span class="comment">// enough to make it positive.</span></div>
<div class="line"><span class="lineno"> 84</span> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 85</span> -b * 0.5 / a, -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"><span class="lineno"> 86</span> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 87</span> -b * 0.5 / a, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> solutions;</div>
<div class="line"><span class="lineno"> 90</span>}</div>
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<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
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