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The image contains algebraic problems written in Indonesian, with equations involving quadratic and other polynomial expressions. Let me translate and solve a few of the problems:

### Problem 2:
**Find the value of \( m \) such that the roots of the equation:**

\[
x^2 + (2m - 1)x + (m^2 - 3m - 4) = 0
\]

**Have the following characteristics:**
a. Both real and opposite \
b. Opposite signs \
c. Both positive

We can approach this by finding the discriminant (\( \Delta \)) and analyzing the properties of the quadratic roots.

### Problem 3:
**Given the equation:**

\[
x^2 + 7x + 9 = 0
\]

Calculate:
a. \( x_1^2 + x_2^2 \) \
b. \( x_1^4 + x_2^4 \) \
c. \( \frac{1}{x_1^3} + \frac{1}{x_2^3} \) \
d. \( x_1^{-4} - x_2^{-4} \)

We will use the sum and product of the roots to find these values.

### Problem 4:
**Given the equation:**

\[
x^2 + 8mx - 2p = 0
\]

Find the value of \( m \) when:
a. \( x_1 = 2x_2 \) \
b. \( 3x_1 = 4x_2 - 1 \) \
c. \( x_1 = -\frac{1}{x_2} \)

These conditions relate to the relationship between the roots and can be solved using algebraic manipulation.

### Problem 5:
**Find the value of \( m \) such that the roots of the equation:**

\[
(m - 4)x^2 - 4(m - 5)x + 9 = 0
\]

Have the following characteristics:
a. Real and unequal \
b. Repeated and positive \
c. Opposite signs \
d. Both negative

This can be solved by analyzing the discriminant and root properties.

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The user submitted a page from a math book written in Indonesian, containing algebraic problems related to quadratic equations and roots.

This problem explores solving quadratic equations with specific conditions on the roots, such as real, positive, opposite, or repeated roots. Detailed steps involve analyzing the discriminant and applying the quadratic formula.

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