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Let's solve the problems step by step.

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### 1. Tentukan nilai **a**, **b**, dan **c** pada persamaan berikut.

We are asked to find the values of **a**, **b**, and **c** from two quadratic equations.

#### a. \( 3x^2 - 5x + 12 = 0 \)

This is in the form of a quadratic equation:

\[
ax^2 + bx + c = 0
\]

- **a** (coefficient of \(x^2\)) = 3
- **b** (coefficient of \(x\)) = -5
- **c** (constant) = 12

So for this equation, the values are:

- \( a = 3 \)
- \( b = -5 \)
- \( c = 12 \)

#### b. \( 4x^2 - 25 = 0 \)

This equation is also quadratic, but it does not have an \(x\) term, which means the coefficient of \(x\) is 0. It can be written as:

\[
4x^2 + 0x - 25 = 0
\]

- **a** (coefficient of \(x^2\)) = 4
- **b** (coefficient of \(x\)) = 0
- **c** (constant) = -25

So for this equation, the values are:

- \( a = 4 \)
- \( b = 0 \)
- \( c = -25 \)

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### 2. Nyatakan persamaan berikut dalam bentuk umum persamaan kuadrat.

Now we need to rewrite the given equations into the standard quadratic form \( ax^2 + bx + c = 0 \).

#### a. \( 6x^2 + 4x - 5 > 4x^2 + 9x \)

Move all terms to one side of the inequality:

\[
6x^2 + 4x - 5 - (4x^2 + 9x) > 0
\]

Simplify:

\[
6x^2 - 4x^2 + 4x - 9x - 5 > 0
\]

\[
2x^2 - 5x - 5 > 0
\]

Thus, the quadratic inequality is:

\[
2x^2 - 5x - 5 > 0
\]

#### b. \( 14y^2 - 7y + 14 = 5y^2 - 7y - 11 \)

Move all terms to one side of the equation:

\[
14y^2 - 7y + 14 - (5y^2 - 7y - 11) = 0
\]

Simplify:

\[
14y^2 - 7y + 14 - 5y^2 + 7y + 11 = 0
\]

\[
(14y^2 - 5y^2) + (-7y + 7y) + (14 + 11) = 0
\]

\[
9y^2 + 25 = 0
\]

Thus, the equation becomes:

\[
9y^2 + 25 = 0
\]

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Would you like a further explanation on any of the steps, or do you have additional questions?

Here are five related questions to help you practice:

1. How do you solve a quadratic equation by factoring?
2. What is the discriminant of a quadratic equation, and how is it used?
3. Can you find the roots of the equation \( 2x^2 - 5x - 5 = 0 \)?
4. How do you solve a quadratic inequality like \( 2x^2 - 5x - 5 > 0 \)?
5. What is the general formula for solving any quadratic equation?

**Tip**: Always move all terms to one side of the equation or inequality to rewrite it in standard form before attempting to solve.

1. Tentukan nilai a, b, dan c pada persamaan berikut. 2. Nyatakan persamaan berikut dalam bentuk umum persamaan kuadrat.

Learn how to determine the values of a, b, and c from quadratic equations like 3x^2 - 5x + 12 = 0 and how to simplify inequalities such as 6x^2 + 4x - 5 > 4x^2 + 9x. This exercise explores key algebraic concepts.

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