document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=785309>Question 785309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> quisiera saber el procedimiento y al respuesta de esta desigualdad -x²+4x-7<0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #477465 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=477465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Los polinomios de grado impar (1, 3, 5, etcétera) cambian de signo por lo menos para un valor de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, siendo negativos de un lado y positivos del otro.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Los polinomios de grado par (2, 4, 6, etcétera) pueden no cambiar de signo nunca.<BR>\n" );
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document.write( "El polinomio de grado 2 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2B4x-7 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > es negativo cuando <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=-7%3C0 ALIGN=MIDDLE  ALT=\"f%280%29=-7%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), así que hay por lo menos <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > es una solución.<BR>\n" );
document.write( "El polinomio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2B4x-7 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > puede ser negativo para todo valor de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, o llegar a ser cero y/o positivo para uno (o más) valores de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Si fuera negativo para algunos pero no todos los valores de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, debería ser cero para algún valor de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Podemos usar la formula para resolver ecuaciones de segundo grado para encontrar si hay ceros. Otra forma de resolver el problema es completar un cuadrado de binomio que incluya los términos en <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "RESOLVIENDO LA ECUACIÓN:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > tiene solución (o soluciones) dadas por<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "si el discriminante, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4%2Aa%2Ac ALIGN=MIDDLE  ALT=\"b%5E2-4%2Aa%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > no es negativo.<BR>\n" );
document.write( "Si el discriminante es negativo, no hay solución real.<BR>\n" );
document.write( "En este caso, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > y <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-7 ALIGN=MIDDLE  ALT=\"c=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4%2Aa%2Ac=4%5E2-4%28-1%29%28-7%29=16-28=-12%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4%2Aa%2Ac=4%5E2-4%28-1%29%28-7%29=16-28=-12%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Así que <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > no tiene solución real.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%5E2%2B4x-7 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%5E2%2B4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > nunca es cero, y nunca cambia de signo; es siempre negativo.<BR>\n" );
document.write( "La solución de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B4x-7%3C0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B4x-7%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > es todo <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > perteneciente a los números reales.<BR>\n" );
document.write( " <BR>\n" );
document.write( "COMPLETANDO EL CUADRADO:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B4x-7=-1%28x%5E2-4x%2B7%29=-1%28x%5E2-4x%2B4%2B3%29=-1%28x%5E2-4x%2B4%29-1%283%29=-%28x-2%29%5E2-3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Como <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%3E=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-2%29%5E2%3C=0 ALIGN=MIDDLE  ALT=\"-%28x-2%29%5E2%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B4x-7=-%28x-2%29%5E2-3%3C=-3 ALIGN=MIDDLE  ALT=\"-x%5E2%2B4x-7=-%28x-2%29%5E2-3%3C=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (para todo valor de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTA:<BR>\n" );
document.write( "Completar el cuadrado es una forma de resolver las ecuaciones de segundo grado sin recurrir a la formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "No requiere memorizar ninguna formula, y a veces es muy fácil.<BR>\n" );
document.write( "Por ejemplo<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B2=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > puede resolverse fácilmente porque sabemos que <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x ALIGN=MIDDLE  ALT=\"x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > es parte del cuadrado de binomio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B2=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x=-2 ALIGN=MIDDLE  ALT=\"x%5E2-4x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B4=-2%2B4 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4=-2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=-2%2B4 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=-2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=2 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Eso significa que <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=sqrt%282%29 ALIGN=MIDDLE  ALT=\"x-2=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"x=2%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, o que<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x-2=-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=2-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A veces no es tan fácil:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B2=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > requiere pensar que <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x ALIGN=MIDDLE  ALT=\"x%5E2-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > es parte de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2=x%5E2-3x%2B9%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2=x%5E2-3x%2B9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x=-1 ALIGN=MIDDLE  ALT=\"x%5E2-3x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B9%2F4=-1%2B9%2F4 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B9%2F4=-1%2B9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%2F2%29%5E2=5%2F4 ALIGN=MIDDLE  ALT=\"%28x-3%2F2%29%5E2=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > y eso lleva a las soluciones<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2+%2B-+sqrt%285%2F4%29 ALIGN=MIDDLE  ALT=\"x=3%2F2+%2B-+sqrt%285%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2+%2B-+sqrt%285%29%2F2=%283+%2B-+sqrt%285%29%29%2F2 ALIGN=MIDDLE  ALT=\"3%2F2+%2B-+sqrt%285%29%2F2=%283+%2B-+sqrt%285%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );