Question

1. Which of the following is not a quadratic equation ?
(a) 2(x - 1)2 = 4x2 – 2x + 1
(6) 2x - x2 = x2 +5
(C) (√2x + √3)2 + x2 = 3x2 – 5x
(d) (x2 + 2x)2 = x4 + 3 + 4x3​

Answer 1

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Answer 2

(√2x + √3)² + x² = 3x² - 5x   is not a quadratic equation

Explanation:

The standard form of a quadratic equation is ax2 + bx + c = 0 in variable x.

Where a, b, and c are real numbers and a ≠ 0.

We need to check if the degree of the given equations is 2.

From the options,

A) 2(x - 1)² = 4x² - 2x + 1

By using algebraic identity,

(a - b)² = a² - 2ab + b²

2(x² + 1 - 2x) = 4x² - 2x + 1

2x² + 2 - 4x = 4x² - 2x + 1

4x² - 2x² - 2x + 4x + 1 - 2 = 0

2x² + 2x - 1 = 0

The degree of the equation is 2.

Therefore, 2(x - 1)² = 4x² - 2x + 1 is a quadratic equation.

B) 2x - x² = x² + 5

x² + x² + 5 - 2x = 0

2x² - 2x + 5 = 0

The degree of the equation is 2.

Therefore, 2x - x² = x² + 5 is a quadratic equation.

C) (√2x + √3)² + x² = 3x² - 5x

By using algebraic identity,

(a + b)² = a² + 2ab + b²

2x² + 3 + 2√6x + x² = 3x² - 5x

By grouping,

3x² - 3x² + 2√6x + 5x + 3 = 0

5x + 2√6x + 3 = 0

The degree of the equation is 1

Therefore, (√2x + √3)² + x² = 3x² - 5x is not a quadratic equation.

D) (x² + 2x)² = x⁴ + 3 + 4x³

By using algebraic identity,

(a + b)² = a² + 2ab + b²

x⁴ + 4x² + 4x³ = x⁴ + 3 + 4x³

Cancelling out common term,

4x² - 3 = 0

The degree of the equation is 2.

Therefore, (x² + 2x)² = x⁴ + 3 + 4x³ is a quadratic equation.