In each of the these question two equation (I) and (II) are given. You have to solve both the equtions and give answer accordingly
I `3x^2+11x+10=0`
II `2y^2+11y+14=0`

Options

A. `xgty`
B. `xgey`
C. `xley`
D. x=y

Answer

To solve the given equations, we will follow these steps:

### Step 1: Solve the first equation \(3x^2 + 11x + 10 = 0\)

1. **Rewrite the equation**: We need to factor the quadratic equation. We can split the middle term (11x) into two parts that add up to 11 and multiply to \(3 \times 10 = 30\).
- The two numbers that work are 5 and 6.
- Rewrite: \(3x^2 + 5x + 6x + 10 = 0\)

2. **Group the terms**:
- Group the first two and the last two terms: \((3x^2 + 5x) + (6x + 10) = 0\)

3. **Factor by grouping**:
- From the first group, factor out \(x\): \(x(3x + 5)\)
- From the second group, factor out 2: \(2(3x + 5)\)
- Combine: \((3x + 5)(x + 2) = 0\)

4. **Set each factor to zero**:
- \(3x + 5 = 0 \Rightarrow x = -\frac{5}{3}\)
- \(x + 2 = 0 \Rightarrow x = -2\)

### Step 2: Solve the second equation \(2y^2 + 11y + 14 = 0\)

1. **Rewrite the equation**: Again, we will factor the quadratic equation. We need two numbers that add up to 11 and multiply to \(2 \times 14 = 28\).
- The two numbers that work are 7 and 4.
- Rewrite: \(2y^2 + 7y + 4y + 14 = 0\)

2. **Group the terms**:
- Group the first two and the last two terms: \((2y^2 + 7y) + (4y + 14) = 0\)

3. **Factor by grouping**:
- From the first group, factor out \(y\): \(y(2y + 7)\)
- From the second group, factor out 2: \(2(2y + 7)\)
- Combine: \((2y + 7)(y + 2) = 0\)

4. **Set each factor to zero**:
- \(2y + 7 = 0 \Rightarrow y = -\frac{7}{2}\)
- \(y + 2 = 0 \Rightarrow y = -2\)

### Summary of Solutions
- For the first equation, the solutions are \(x = -\frac{5}{3}\) and \(x = -2\).
- For the second equation, the solutions are \(y = -\frac{7}{2}\) and \(y = -2\).

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

- We have \(x\) values: \(-\frac{5}{3} \approx -1.67\) and \(-2\).
- We have \(y\) values: \(-\frac{7}{2} = -3.5\) and \(-2\).

### Conclusion
- The values of \(x\) and \(y\) show that:
- For \(x = -\frac{5}{3}\), \(y = -\frac{7}{2}\) gives \(x > y\).
- For \(x = -2\), \(y = -2\) gives \(x = y\).

Thus, we conclude that \(x \geq y\).

### Final Answer
The correct answer is \(x \geq y\).

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