Decide which of the following are quadratic i. x2 – 7y + 2 = 0 ii.

1.	Decide which of the following are quadratic i. x2 – 7y + 2 = 0 ii. y2 = 5y – 10 iii. y2 + 1/y = 2
Answer» i. The given equation is x² + 5x – 2 = 0 Here, x is the only variable and maximum index of the variable is 2. a = 1, b = 5, c = -2 are real numbers and a ≠ 0. ∴ The given equation is a quadratic equation. ii. The given equation is y² = 5y – 10 ∴ y² – 5y + 10 = 0 Here, y is the only variable and maximum index of the variable is 2. a = 1, b = -5, c = 10 are real numbers and a ≠ 0. ∴ The given equation is a quadratic equation. iii. The given equation is y² + 1/y = 2 ∴ y³ + 1 = 2y …[Multiplying both sides by y ] ∴ y³ – 2y + 1 = 0 Here, y 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 quadratic i. x2 – 7y + 2 = 0 ii. y2 = 5y – 10 iii. y2 + 1/y = 2

Answer»

i. The given equation is x² + 5x – 2 = 0

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

a = 1, b = 5, c = -2 are real numbers and a ≠ 0.

∴ The given equation is a quadratic equation.

ii. The given equation is

y² = 5y – 10

∴ y² – 5y + 10 = 0

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

a = 1, b = -5, c = 10 are real numbers and a ≠ 0.

∴ The given equation is a quadratic equation.

iii. The given equation is

y² + 1/y = 2

∴ y³ + 1 = 2y …[Multiplying both sides by y ]

∴ y³ – 2y + 1 = 0 Here,

y is the only variable and maximum index of the variable is not 2.

∴ The given equation is not a quadratic equation.