5) Indicar la suma de las coordenadas que logra minimizar a la función cuadrática: f(x) = 3 x2 – 2x + 7
Respuestas a la pregunta
1 En general, dado
a{x}^{2}+bx+cax 2
+bx+c, la forma factorizada es:
a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})
a(x−
2a
−b+
b
2
−4ac
)(x−
2a
−b−
b
2
−4ac
)
2 En este caso, a=3a=3, b=-2b=−2 y c=7c=7.
3(x-\frac{2+\sqrt{{(-2)}^{2}-4\times 3\times 7}}{2\times 3})(x-\frac{2-\sqrt{{(-2)}^{2}-4\times 3\times 7}}{2\times 3})
3(x−
2×3
2+
(−2)
2
−4×3×7
)(x−
2×3
2−
(−2)
2
−4×3×7
)
3 Simplifica.
3(x-\frac{2+4\sqrt{5}\imath }{6})(x-\frac{2-4\sqrt{5}\imath }{6})
3(x−
6
2+4
5
)(x−
6
2−4
5
)
4 Extrae el factor común 22.
3(x-\frac{2(1+2\sqrt{5}\imath )}{6})(x-\frac{2-4\sqrt{5}\imath }{6})
3(x−
6
2(1+2
5
)
)(x−
6
2−4
5
)
5 Simplifica \frac{2(1+2\sqrt{5}\imath )}{6}
6
2(1+2
5
)
a \frac{1+2\sqrt{5}\imath }{3}
3
1+2
5
.
3(x-\frac{1+2\sqrt{5}\imath }{3})(x-\frac{2-4\sqrt{5}\imath }{6})
3(x−
3
1+2
5
)(x−
6
2−4
5
)
6 Extrae el factor común 22.
3(x-\frac{1+2\sqrt{5}\imath }{3})(x-\frac{2(1-2\sqrt{5}\imath )}{6})
3(x−
3
1+2
5
)(x−
6
2(1−2
5
)
)
7 Simplifica \frac{2(1-2\sqrt{5}\imath )}{6}
6
2(1−2
5
)
a \frac{1-2\sqrt{5}\imath }{3}
3
1−2
5
.
3(x-\frac{1+2\sqrt{5}\imath }{3})(x-\frac{1-2\sqrt{5}\imath }{3})
3(x−
3
1+2
5
)(x−
3
1−2
5
)
Hecho