Question

Find a quartic equation having the double roots 2, -2?

Answer 1

The roots of the quartic equation are: double roots 2, -2 ie the roots are, 2, 2, -2, -2.

The quartic equation would be

(x - 2)(x - 2)(x + 2)(x + 2) = 0

⇒ (x - 2)(x + 2)(x — 2)(x + 2) = 0

⇒ [x² - 2²][x² - 2²] = 0

⇒ (x² - 4)² = 0

⇒ x⁴ - 2. 4. x² + 4² = 0

⇒ x⁴ - 8 x² + 16 = 0