In each question, two equations numbered I and II have been given. you have to solve both the equations and mark the appropiate option.
I `15x^2+26x+8=0`
II `25y^2+15y+2=0`

Options

A. `xgty`
B. `xley`
C. x = yor no relation can be established between x and-y
D. `xgey`

Answer

To solve the given quadratic equations step by step, we will follow a structured approach for each equation.

### Step 1: Solve the first equation \(15x^2 + 26x + 8 = 0\)

1. **Identify coefficients**:
- Here, \(a = 15\), \(b = 26\), and \(c = 8\).

2. **Use the quadratic formula**:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = 26^2 - 4 \cdot 15 \cdot 8 = 676 - 480 = 196 \]

4. **Find the roots**:
\[ x = \frac{-26 \pm \sqrt{196}}{2 \cdot 15} = \frac{-26 \pm 14}{30} \]
- First root:
\[ x_1 = \frac{-26 + 14}{30} = \frac{-12}{30} = -\frac{2}{5} \]
- Second root:
\[ x_2 = \frac{-26 - 14}{30} = \frac{-40}{30} = -\frac{4}{3} \]

### Step 2: Solve the second equation \(25y^2 + 15y + 2 = 0\)

1. **Identify coefficients**:
- Here, \(a = 25\), \(b = 15\), and \(c = 2\).

2. **Use the quadratic formula**:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = 15^2 - 4 \cdot 25 \cdot 2 = 225 - 200 = 25 \]

4. **Find the roots**:
\[ y = \frac{-15 \pm \sqrt{25}}{2 \cdot 25} = \frac{-15 \pm 5}{50} \]
- First root:
\[ y_1 = \frac{-15 + 5}{50} = \frac{-10}{50} = -\frac{1}{5} \]
- Second root:
\[ y_2 = \frac{-15 - 5}{50} = \frac{-20}{50} = -\frac{2}{5} \]

### Step 3: Compare the values of \(x\) and \(y\)

- The values obtained are:
- For \(x\): \(-\frac{2}{5}\) and \(-\frac{4}{3}\)
- For \(y\): \(-\frac{1}{5}\) and \(-\frac{2}{5}\)

### Conclusion:

- Comparing the values:
- \(-\frac{2}{5} \) (from \(x\)) and \(-\frac{1}{5}\) (from \(y\)): \(-\frac{2}{5} < -\frac{1}{5}\)
- \(-\frac{4}{3} < -\frac{2}{5}\)

Thus, we can conclude that \(x\) is less than or equal to \(y\).

### Final Answer:
The correct option is \(x \leq y\).

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