Question

Decide which of the following are quadratic

i. x + 1/x = -2

ii. (m + 2) (m – 5) = 0

iii. m³ + 3m² – 2 = 3m³

Answer 1

i. The given equation is

x + 1/x = -2

∴ x² + 1 = -2x …[Multiplying both sides by x]

∴ x² + 2x+ 1 = 0

Here, x is the only variable and maximum index of the variable is 2.

a = 1, b = 2, c = 1 are real numbers and a ≠ 0.

∴ The given equation is a quadratic equation.

ii. The given equation is 

(m + 2) (m – 5) = 0 

∴ m(m – 5) + 2(m – 5) = 0 

∴ m² – 5m + 2m – 10 = 0 

∴ m² – 3m – 10 = 0

Here, m is the only variable and maximum index of the variable is 2.

a = 1, b = -3, c = -10 are real numbers and a ≠ 0.

∴ The given equation is a quadratic equation.

iii. The given equation is

m³ + 3m² – 2 = 3m 

∴ 3m³ – m³ – 3m² + 2 = 0 

∴ 2m³ – 3m² + 2 = 0

Here, m is the only variable and maximum index of the variable is not 2.

∴ The given equation is not a quadratic equation.