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<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">z</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="quin_1.html#K2">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="polyeq_1.html#K7">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,0,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:16"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="polyeq_3.html#K1" target="_self">*</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="polyeq_3.html#K3" target="_self">^2</a> </span>)</span></span>)</span> <a href="complex1.html#K8">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="polyeq_3.html#K1" target="_self">*</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E3:16"/><b>then </b>
(  <a href="polyeq_3.html#K4" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<b>hence </b><a NAME="E4:16"/>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K2">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> <font color="Maroon">b</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K2">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">z</font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> or <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, </i>;<br/>


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