Decide which of the following are quadratic equations: (1) x^2 + 5x - 2 = 0 (2) y^2 = 5y - 10 (3) y^2 + 1/y = 2 (4) x + 1/x = -2 (5) (m + 2)(m - 5) = 0 (6) m^3 + 3m^2 - 2 = 3m^3

Answer: (1), (2), (4) and (5) are quadratic equations; (3) and (6) are not.

• (1) \(x^2 + 5x - 2 = 0\): highest index 2, so quadratic.
• (2) \(y^2 - 5y + 10 = 0\): quadratic.
• (3) Multiplying by \(y\) gives \(y^3 - 2y + 1 = 0\), index 3: not quadratic.
• (4) Multiplying by \(x\) gives \(x^2 + 2x + 1 = 0\): quadratic.
• (5) \(m^2 - 3m - 10 = 0\): quadratic.
• (6) \(-2m^3 + 3m^2 - 2 = 0\): the \(m^3\) term remains, so it is not quadratic.