**(1) x ^{2} + 5x – 2 = 0**

**Solution:**

x^{2} + 5x – 2 = 0 is a quadratic equation because it is the form of ax^{2} + bx + c = 0 and it has degree 2.

**(2) y ^{2} = 5y – 10**

**Solution:**

y^{2} = 5y – 10 is a quadratic equation because it is the form of ax^{2} + bx + c = 0 and it has degree 2.

**(3) y ^{2} + 1/y = 2**

**Solution:**

y^{2} + 1/y = 2 is a quadratic equation because it is the form of ax^{2} + bx + c = 0 and it has degree 2.

**(4) x + 1/x = -2**

**Solution:**

Given equation can be written as

x^{2} + 1 = -2x

x^{2} + 2x + 1 = 0

It is a quadratic equation because it is the form of ax^{2} + bx + c = 0 and it has degree 2.

**(5) (m + 2) (m–5) = 0**

**Solution:**

Given equation can be written as

m (m – 5) + 2 (m – 5)

= m^{2} – 5m + 2m – 10

= m^{2 }– 3m + 10 = 0

It is a quadratic equation because it is the form of ax^{2} + bx + c = 0 and it has degree 2.

**(6) m ^{3} + 3m^{2} – 2 = 3 m^{3}**

**Solution:**

Given m^{3} + 3m^{2} – 2 = 3 m^{3}

It is not a quadratic equation because it is not in the form of ax^{2} + bx + c = 0 and it has degree 3.