Which of the following expression is a quadratic polynomial?

Options

A. `2x+3`
B. `3x^(2)-5x+4`
C. `(1)/(2x^(2)+3x+5)`
D. None of these.

Explanation

To determine which of the given expressions is a quadratic polynomial, we need to understand the definition of a quadratic polynomial. A quadratic polynomial is a polynomial of degree 2, which means the highest power of the variable (usually denoted as \(x\)) is 2. Additionally, a polynomial can only contain non-negative integer powers of the variable, and the coefficients must be real numbers.

Let's analyze the options step by step:

### Step 1: Identify the expressions
Assuming we have four expressions to evaluate, we will denote them as:
1. Expression 1: \(x + 2\)
2. Expression 2: \(3x^2 - 5x + 4\)
3. Expression 3: \(\frac{1}{x}\)
4. Expression 4: \(x^3 + 2x^2 + 1\)

### Step 2: Analyze each expression

**Expression 1: \(x + 2\)**
- The highest power of \(x\) is 1.
- Since the degree is not 2, this is not a quadratic polynomial.

**Expression 2: \(3x^2 - 5x + 4\)**
- The highest power of \(x\) is 2.
- This expression meets the criteria for a quadratic polynomial (degree 2).
- Therefore, this is a quadratic polynomial.

**Expression 3: \(\frac{1}{x}\)**
- This can be rewritten as \(x^{-1}\).
- The power of \(x\) is -1, which is not a non-negative integer.
- Therefore, this is not a quadratic polynomial.

**Expression 4: \(x^3 + 2x^2 + 1\)**
- The highest power of \(x\) is 3.
- Since the degree is not 2, this is not a quadratic polynomial.

### Conclusion
From the analysis, the only expression that qualifies as a quadratic polynomial is **Expression 2: \(3x^2 - 5x + 4\)**.

### Final Answer
The quadratic polynomial among the given expressions is **\(3x^2 - 5x + 4\)**.

---