Decide which of the following are quadratici. x + 1/x = -2ii. (m + 2)

1.	Decide which of the following are quadratici. x + 1/x = -2ii. (m + 2) (m – 5) = 0iii. m3 + 3m2 – 2 = 3m3
Answer» 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.

Decide which of the following are quadratici. x + 1/x = -2ii. (m + 2) (m – 5) = 0iii. m3 + 3m2 – 2 = 3m3

Answer»

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.