I see whether the following equations can be written in the form of ax^2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0

Question

I see whether the following equations can be written in the form of ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0

(iv) (x – 2)² = x³ – 4x + 4

(v) (x – 3)³ = 2x (x² – 1)

Answer:

(iv) (x – 2)² = x³ – 4x + 4

or, x² – 4x + 4 = x³ – 4x + 4

or, x² – x³ = 0

This is not a quadratic equation, as it is not in the form ax² + bx + c = 0

(v) (x – 3)³ = 2x (x² – 1)

or, x³ – 9x² + 27x + 27 = 2x³ – 2x

or, – x³ – 9x² + 29x + 27 = 0

This is not a quadratic equation, as it is not in the form ax² + bx + c = 0