Question

The expression x⁴ – 2x² + k will be a perfect square, when the value of k is.

1. 2
2. 1
3. -1
4. -2

Answer 1

Correct Answer - Option 2 : 1

Given :

Expression is x4 – 2x2 + k

Formula Used :

A quadratic expression ax² + bx + c, a ≠ 0 is a perfect square, when

b² - 4ac = 0

Calculation :

Given expression is x4 – 2x2 + k

⇒ (x²)² - 2x² + k

Let the value of x² be y 

 ⇒ y² - 2y + k 

On comparing quadratic expression we get a = 1, b = -2 and c = k

According to the question, this expression is a perfect square 

 ⇒ b2 - 4ac = 0 

⇒ (-2)² - 4 × 1 × k = 0

⇒ 4 - 4k = 0

⇒ k = 1

∴ The value of k is 1.