▶️ Ejercicio 278 álgebra - Solucionario Baldor ✅✅

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CAPITULO XXXV

Dadas las raíces de una ecuación de segundo grado, determinar la ecuación

Ejercicio 278

Determinar la ecuación cuyas raíces son:

3 y 4
$\begin{matrix} 3 + 4 & = 7 \\ \land & \Rightarrow x^{2} - 7 x + 12 = 0 \\ 3 (4) & = 12 \end{matrix}$
-1 y 3
$\begin{matrix} - 1 + 3 & = 2 \\ \land & \Rightarrow x^{2} - 2 x - 3 = 0 \\ - 1 (3) & = - 3 \end{matrix}$
-5 y -7
$\begin{matrix} - 5 - 7 & = - 12 \\ \land & \Rightarrow x^{2} + 12 x + 35 = 0 \\ - 5 (- 7) & = 35 \end{matrix}$
-10 y 11
$\begin{matrix} - 10 + 11 & = 1 \\ \land & \Rightarrow x^{2} - x + 110 = 0 \\ - 10 (11) & = 110 \end{matrix}$
1 y $\frac{1}{2}$
$\begin{matrix} 1 + \frac{1}{2} & = \frac{3}{2} \\ \land & \Rightarrow x^{2} - \frac{3}{2} x + \frac{1}{2} = 0 \leftrightarrow 2 x^{2} - 3 x + 1 = 0 \\ 1 (\frac{1}{2}) & = \frac{1}{2} \end{matrix}$
-2 y $- \frac{1}{5}$
$\begin{matrix} - 2 - \frac{1}{5} & = - \frac{11}{5} \\ \land & \Rightarrow x^{2} + \frac{11}{5} x + \frac{2}{5} = 0 \leftrightarrow 5 x^{2} + 11 x + 2 = 0 \\ - 2 (- \frac{1}{5}) & = \frac{2}{5} \end{matrix}$
3 y $- \frac{2}{3}$
$\begin{matrix} 3 - \frac{2}{3} & = \frac{7}{3} \\ \land & \Rightarrow x^{2} - \frac{7}{3} x + 1 = 0 \leftrightarrow 3 x^{2} - 7 x + 3 = 0 \\ 3 (\frac{1}{3}) & = 1 \end{matrix}$
-2 y $- \frac{3}{2}$
$\begin{matrix} - 2 - \frac{3}{2} & = - \frac{7}{2} \\ \land & \Rightarrow x^{2} + \frac{7}{2} x + 3 = 0 \leftrightarrow 2 x^{2} + 7 x + 6 = 0 \\ - 2 (- \frac{3}{2}) & = 3 \end{matrix}$
$- \frac{1}{2}$ y $\frac{3}{4}$
$\begin{matrix} - \frac{1}{2} + \frac{3}{4} & = \frac{1}{4} \\ \land & \Rightarrow x^{2} - \frac{1}{4} x - \frac{3}{8} = 0 \leftrightarrow 8 x^{2} - 2 x - 3 = 0 \\ - \frac{1}{2} (\frac{3}{4}) & = - \frac{3}{8} \end{matrix}$
-5 y $\frac{2}{7}$
$\begin{matrix} - 5 + \frac{2}{7} & = - \frac{33}{7} \\ \land & \Rightarrow x^{2} + \frac{33}{7} x - \frac{10}{7} = 0 \leftrightarrow 7 x^{2} + 33 x - 10 = 0 \\ - 5 (\frac{2}{7}) & = - \frac{10}{7} \end{matrix}$
6 y $- \frac{5}{3}$
$\begin{matrix} 6 - \frac{5}{3} & = \frac{13}{3} \\ \land & \Rightarrow x^{2} - \frac{13}{3} x - 10 = 0 \leftrightarrow 3 x^{2} - 13 x - 30 = 0 \\ (- \frac{5}{3}) & = - 10 \end{matrix}$
-2 y $- \frac{1}{8}$
$\begin{matrix} - 2 - \frac{1}{8} & = - \frac{17}{8} \\ \land & \Rightarrow x^{2} + \frac{17}{8} x + \frac{1}{4} = 0 \leftrightarrow 8 x^{2} + 17 x + 2 = 0 \\ - 2 (- \frac{1}{}) & = \frac{1}{4} \end{matrix}$
18 y -52
$\begin{matrix} 18 - 52 & = - 34 \\ \land & \Rightarrow x^{2} + 34 x + 936 = 0 \\ 18 (- 52) & = 936 \end{matrix}$
-15 y -11
$\begin{matrix} - 15 - 11 & = - 26 \\ \land & \Rightarrow x^{2} + 26 x + 165 = 0 \\ - 15 (- 11) & = 165 \end{matrix}$
0 y 2
$\begin{matrix} 0 + 2 & = 2 \\ \land & \Rightarrow x^{2} - 2 x = 0 \\ 0 (2) & = 0 \end{matrix}$
0 y $- \frac{1}{3}$
$\begin{matrix} 0 - \frac{1}{3} & = - \frac{1}{3} \\ \land & \Rightarrow x^{2} + \frac{1}{3} x = 0 \leftrightarrow 3 x^{2} + x = 0 \\ 0 (- \frac{1}{3}) & = 0 \end{matrix}$
5 y -5
$\begin{matrix} 5 - 5 & = 0 \\ \land & \Rightarrow x^{2} - 25 = 0 \\ 5 (- 5) & = - 25 \end{matrix}$
$\frac{1}{2}$ y $- \frac{1}{2}$
$\begin{matrix} \frac{1}{2} - \frac{1}{2} & = 0 \\ \land & \Rightarrow x^{2} - \frac{1}{4} = 0 \leftrightarrow 4 x^{2} - 1 = 0 \\ \frac{1}{2} (- \frac{1}{2}) & = - \frac{1}{4} \end{matrix}$
7 y 7
$\begin{matrix} 7 + 7 & = 14 \\ \land & \Rightarrow x^{2} - 14 x + 49 = 0 \\ 7 (7) & = 49 \end{matrix}$
8 y $- \frac{11}{3}$
$\begin{matrix} 8 - \frac{11}{3} & = \frac{13}{3} \\ \land & \Rightarrow x^{2} - \frac{13}{3} x - \frac{88}{3} = 0 \leftrightarrow 3 x^{2} - 13 x - 88 = 0 \\ 8 (- \frac{11}{3}) & = - \frac{88}{3} \end{matrix}$
$- \frac{5}{6}$ y $- \frac{9}{2}$
$\begin{matrix} - \frac{5}{6} - \frac{9}{2} & = - \frac{16}{3} \\ \land & \Rightarrow x^{2} + \frac{16}{3} x + \frac{15}{4} = 0 \leftrightarrow 12 x^{2} + 64 x + 45 = 0 \\ - \frac{5}{} (- \frac{}{2}) & = \frac{15}{4} \end{matrix}$
$- \frac{11}{2}$ y $\frac{2}{7}$
$\begin{matrix} - \frac{11}{2} + \frac{2}{7} & = - \frac{73}{14} \\ \land & \Rightarrow x^{2} + \frac{73}{14} x - \frac{11}{7} = 0 \leftrightarrow 14 x^{2} + 73 x - 22 = 0 \\ - \frac{11}{2} (\frac{2}{7}) & = - \frac{11}{7} \end{matrix}$
2a y -a
$\begin{matrix} 2 a - a & = a \\ \land & \Rightarrow x^{2} - a x - 2 a^{2} = 0 \\ 2 a (- a) & = - 2 a^{2} \end{matrix}$
$- \frac{2 b}{3}$ y $\frac{b}{4}$
$\begin{matrix} - \frac{2 b}{3} + \frac{b}{4} & = - \frac{5}{12} b \\ \land & \Rightarrow x^{2} + \frac{5}{12} b x - \frac{b^{2}}{6} = 0 \leftrightarrow 12 x^{2} + 5 b x - 2 b^{2} = 0 \\ - \frac{2 b}{3} (\frac{b}{}) & = - \frac{b^{2}}{6} \end{matrix}$
m y $- \frac{m}{2}$
$\begin{matrix} m - \frac{m}{2} & = \frac{m}{2} \\ \land & \Rightarrow x^{2} - \frac{m}{2} x - \frac{m^{2}}{2} = 0 \leftrightarrow 2 x^{2} - m x - m^{2} = 0 \\ m (- \frac{m}{2}) & = - \frac{m^{2}}{2} \end{matrix}$

Categories: Capítulo XXXV