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Home Question Bank Math Algebra Archive 2024 December 31

Algebra Questions from Dec 31,2024

Browse the Algebra Q&A Archive for Dec 31,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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ecuaciones cuadráticas 3. \( 3 x^{2}-6=x^{2}+2 \) 4. \( (x+6)(x-6)=13 \) 1. \( x^{2}-9=0 \) \( \begin{array}{ll}\text { calcula la solucion de las siguientes ecuaciones cuadráticas. } \\ \text { 2. } 4 x^{2}-16=0 & 4 \cdot(x+6)(x-6)=13\end{array} \) ansformemes SEGEY Dirección de Educación Media Superior Departamento de Servicios Educativos Si la gráfica de una ecuación cuadrática corta el eje \( x \) en dos puntos, significa que el discriminante es: \( \qquad \) Si la gráfica de una ecuación cuadrática corta el eje \( x \) en un punto, significa que el discriminante es: \( \qquad \) (1) If \( (g \circ f)(x)=x^{2}+x+6 \) and \( f(x)=x+2 \), then \( g(x) \) is equal to _- (A) \( x^{2}-3 x+8(\mathrm{~B})-x^{2}-3 x+6(\mathrm{C}) x^{2}+3 x+8 \) (D) \( x^{2}-3 x-6 \) (2) Which one of the following is False about the relation \( R=\left\{(x, y): y=\frac{x+3}{x+10}\right\} \) ? (A) The Range of \( R \) is \( (-\infty,-1) \cup(1, \infty) \). (B) The \( R \) Domain of \( R \) is \( (-\infty,-10) \cup(-10, \infty) \). (C) \( R=\left\{(x, y): y=\frac{x+3}{x+10}\right\} \) is a function. (D) The inverse of \( R \) is \( \left\{(y, x): y=\frac{10 x+3}{x+1}\right\} \). (3) If the standard deviation of \( x_{1}, x_{2}, x_{3}, \cdots, x_{n} \) is 3 , then what is the standard deviatio Exercise 8. \( \star \) We define on \( \mathbb{R}^{2} \) the binary operation \( \oplus \) as follows: \[ \forall(x, y),\left(x^{\prime}, y^{\prime}\right) \in \mathbb{R}^{2},(x, y) \oplus\left(x^{\prime}, y^{\prime}\right)=\left(x+x^{\prime}, y+y^{\prime}+2 x x^{\prime}\right) . \] Show that \( \left(\mathbb{R}^{2}, \oplus\right) \) is an abelian group. 2 Show that \( H=\left\{\left(x, x^{2}\right) \mid x \in \mathbb{R}\right\} \) is a subgroup of \( \left(\mathbb{R}^{2}, \oplus\right) \). 3. Show that the map \( \oplus:(\mathbb{R},+) \longrightarrow(H, \oplus) \) defined by \( \oplus(x)=\left(x, x^{2}\right) \) is an isomorphism of groups. \begin{tabular}{|ll}\hline I. & Descripción de \\ 1. & Es la forma general de una ecuación cuadrática \\ 2. & Es la representación de una ecuación cuadrática \\ 3. Es la representación de una ecuación cuadrática \\ 4. Escribe la fórmula general para obtener las raices \\ 5. Es la expresión que representa al discriminante d \\ 6. Si el discriminante es mayor que cero: \( b^{2}-4 a \) \\ grado? \\ 7. Si el discriminante es menor que cero: \( b^{2}-4 a \) \\ grado? \\ 8. Si el discriminante es igual que cero: \( b^{2}-4 a \) \\ grado? \end{tabular} Regla de Ruffini Factorizacion de Polinomios \( x^{4}-x^{3}+2 x^{2}+4 x-8=0 \) If \( L \) and \( M \) are the roots of the equation: \( x^{2}-2 x+4=0 \), then \( \sqrt{L}+\sqrt{M}=\ldots \) \( \begin{array}{llll}\text { (a) } 1 & \text { (b) } \sqrt{6} & \text { (c) } 2 & \text { (d) } \sqrt{2}\end{array} \) Regla de Ruffini Factorizacion de Polinomios \( x^{4}-x^{3}-13 x^{2}+25 x-12=0 \) (a) \( x^{2}-8 x+15=0 \)
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