Question

If x⁴ – 5x² + 4 = 0; the values of x are ______.

Options

• 1 or 2

• ±1 or ±2

• –1 and 2

• –1 and –2

Answer 1

If x⁴ – 5x² + 4 = 0; the values of x are ±1 or ±2.

Explanation:

Given quadratic equation be,

x⁴ – 5x² + 4 = 0   ...(1)

Put x² = t in equation (1); we have

t² – 5t + 4 = 0

`\implies` t² – 4t – t + 4 = 0

`\implies` t(t – 4) – 1(t – 4) = 0

`\implies` (t – 1)(t – 4) = 0

Either t – 1 = 0 or t – 4 = 0

`\implies` t = 1 or t = 4

`\implies` x² = 1 or x² = 4

`\implies` x = ±1 or x = ±2

`\implies` x = ±1 or ±2