Question

Which of the following is not a quadratic equation?

विकल्प

• (x + 2)² = 2(x + 3)

• x² + 3x = (–1)(1 – 3x²)

• (x + 2)(x – 1) = x² – 2x – 3

• x³ – x² + 2x + 1 = (x + 1)³

Answer 1

(x + 2)(x – 1) = x² – 2x – 3

Explanation:

Simplify each equation:

1) (x + 2)² = 2(x + 3)

Expand the equation:

x² + 4x + 4 = 2x + 6

Rearrange to standard form: 

x² + 2x – 2 = 0

This is a quadratic equation.

2) x² + 3x = (–1)(1 – 3x²)

Expand the equation:

x² + 3x = −1 + 3x²

Rearrange to standard form:

−2x² + 3x + 1 = 0

This is a quadratic equation.

3) (x + 2)(x – 1) = x² – 2x – 3

Expand the left side:

x² + x – 2 = x² – 2x – 3

When you subtract x² from both sides, the quadratic term is eliminated.

Rearrange to standard form: 

3x + 1 = 0

This is a linear equation, not a quadratic one.

4) x³ – x² + 2x + 1 = (x + 1)³

Expand the right side using the formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

x³ – x² + 2x + 1

Set them equal:

x³ − 2x + x + 1 = x³ + 3x² + 3x + 1

When you subtract x³ from both sides, the cubic term is eliminated.

Rearrange to standard form:

−4x² − x = 0

This is a quadratic equation.