i. The given equation is
x2 + 2x + 11 = 0
Here, x is the only variable and maximum index of the variable is 2.
a = 1, b = 2, c = 11 are real numbers and a ≠ 0.
The given equation is a quadratic equation.
ii. The given equation is
x2 – 2x + 5 = x2
∴ x2 – x2 + 2x – 5 = 0
∴ 2x – 5 = 0
Here, x is the only variable and maximum index of the variable is not 2.
∴ The given equation is not a quadratic equation.
iii. The given equation is
(x + 2)2 = 2x2
∴ x2 + 4x + 4 = 2x2
∴ 2x2 – x2 – 4x – 4 = 0
∴ x2 – 4x – 4 = 0
Here, x is the only variable and maximum index of the variable is 2.
a = 1, b = -4, c = —4 are real numbers and a ≠ 0.
∴ The given equation is a quadratic equation.