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The image contains the following quadratic equation problem in Indonesian:

**"Pada persamaan kuadrat \( ax^2 - 7x + 3 = 0 \), salah satu akarnya adalah 3. Maka akar lainnya adalah ..."**

Translation:
"In the quadratic equation \( ax^2 - 7x + 3 = 0 \), one of the roots is 3. What is the other root?"

### Step-by-step solution:

The quadratic equation is given as:
\[
ax^2 - 7x + 3 = 0
\]
One root is known: \( x = 3 \). We will use this information to find the value of \( a \) and then the other root.

1. **Use Vieta's formulas**:
   - The sum of the roots is given by \( -\frac{b}{a} \).
   - The product of the roots is given by \( \frac{c}{a} \).

In our case, the equation is in the form \( ax^2 - 7x + 3 = 0 \), so:
- \( b = -7 \)
- \( c = 3 \)

Let the other root be \( r \). From Vieta's formulas:
\[
\text{Sum of roots} = 3 + r = \frac{-(-7)}{a} = \frac{7}{a}
\]
Thus, \( 3 + r = \frac{7}{a} \).

2. **Find \( a \) by using the given root \( x = 3 \)**:
Substitute \( x = 3 \) into the quadratic equation:
\[
a(3)^2 - 7(3) + 3 = 0
\]
This simplifies to:
\[
9a - 21 + 3 = 0
\]
\[
9a - 18 = 0
\]
\[
9a = 18
\]
\[
a = 2
\]

3. **Find the other root \( r \)**:
Now that we know \( a = 2 \), we can substitute into the sum of roots equation:
\[
3 + r = \frac{7}{2}
\]
\[
r = \frac{7}{2} - 3 = \frac{7}{2} - \frac{6}{2} = \frac{1}{2}
\]

Thus, the other root is **\( \frac{1}{2} \)**.

---

Would you like any more details or have any questions?

Here are some related questions to consider:
1. How do you derive Vieta's formulas for quadratic equations?
2. How can you solve a quadratic equation using the quadratic formula?
3. How does changing the value of \( a \) affect the shape of the parabola in a quadratic equation?
4. What are the possible types of roots a quadratic equation can have?
5. How can you factor a quadratic equation when one root is known?

**Tip**: When solving quadratic equations, always double-check if the given root satisfies the equation before proceeding with further steps.

Pada persamaan kuadrat ax^2 - 7x + 3 = 0, salah satu akarnya adalah 3. Maka akar lainnya adalah ...

Learn how to solve the quadratic equation ax^2 - 7x + 3, where one root is given as 3. This problem uses Vieta's formulas to find the other root, covering key algebraic concepts such as the sum and product of roots.

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