Decide which of the following are quadratic equations.

(1) x² + 5x – 2 = 0

Solution:
x² + 5x – 2 = 0 is a quadratic equation because it is the form of ax² + bx + c = 0 and it has degree 2.

(2) y² = 5y – 10

Solution:
y² = 5y – 10 is a quadratic equation because it is the form of ax² + bx + c = 0 and it has degree 2.

(3) y² + 1/y = 2

Solution:
y² + 1/y = 2 is a quadratic equation because it is the form of ax² + bx + c = 0 and it has degree 2.

(4) x + 1/x = -2

Solution:
Given equation can be written as
x² + 1 = -2x
x² + 2x + 1 = 0
It is a quadratic equation because it is the form of ax² + 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)
= m² – 5m + 2m – 10
= m² – 3m + 10 = 0
It is a quadratic equation because it is the form of ax² + bx + c = 0 and it has degree 2.

(6) m³ + 3m² – 2 = 3 m³

Solution:
Given m³ + 3m² – 2 = 3 m³
It is not a quadratic equation because it is not in the form of ax² + bx + c = 0 and it has degree 3.