Which of the followings is a second degree polynomial?

For option (a),

We have √x – 4.

Observe the two terms, x has an exponent of 1/2.

But for second degree polynomials, the degree should be 2 (that is, largest exponent of x should be 2)

⇒ √x – 4 is not a second degree polynomial.

For option (b),

We have x³ + x.

The degree of this expression is 3 (largest exponent of x is 3).

But for second degree polynomials, the degree should be 2 (that is, largest exponent of x should be 2)

⇒ x³ + x is not a second degree polynomial.

For option (c),

We have x³ + 2x + 6.

The degree of this expression is also 3 (largest exponent of x is 3).

But for second degree polynomials, the degree should be 2 (that is, largest exponent of x should be 2)

⇒ x³ + 2x + 6 is not a second degree polynomial.

For option (d),

We have x² + 5x + 6.

The degree of this expression is 2 (largest exponent of x is 2).

This satisfies the criteria of second degree polynomial.

⇒ x² + 5x + 6 is second degree polynomial.

Thus, option (d) is correct.