1 The cubic polynomial \( f(x) \) is given by \( f(x)=2 x^{3}+a x^{2}+b x+c \), where \( a, b, c \) are constants. The graph of \( f(x) \) intersects the \( x \)-axis at the points with coordinates \( (-3,0),(2 \cdot 5,0) \) and \( (4,0) \). Find the coordinates of the point where the graph of \( f(x) \) intersects the \( y \)-axis.

2 - Qual é o valor de \( x \) \( \begin{array}{ll}\text { a) } 2^{x}=32 & \text { b) } 5^{a}=25\end{array} \)

2 - Qual é o valor de \( x \) \( \begin{array}{ll}\text { a) } 2^{x}=32 & \text { b) } 5^{a}=25\end{array} \)

10. a. Show that the roots of the equation \( 2\left(a^{2}+b^{2}\right) x^{2}+2(a+b) x+1=0 \) can never be real unless \( a=b \). b. Prove that the roots of the equation \( x^{2}+(2 k-1) x+k^{2}=0 \) are real roots if \( k \leq \frac{1}{4} \).

e. Qual i o valor de \( x \) \( \begin{array}{ll}\text { a) } 2^{x}=32 & \text { b) } 5^{x}=25\end{array} \)

27. Dada la matriz \( A=\left[\begin{array}{cc}a & b \\ -b & a\end{array}\right] \) [video guia: https://voutu.be/m580)hu2MnIPsi=t|Gfe9fJKvVSr7KH] a. Determine valores propios y los vectores propios complejos asociados b. Encuentre los valores caracteristicos de la matriz \( B=A^{T} A \) c. Si los valores caracteristicos de \( \left[\begin{array}{ll}a & b \\ 0 & d\end{array}\right] \) son 0 y 1 , halle los posibles valores de \( a \) y \( d \)