Question

For the following polynomial, one zero is given. Find the remaining zeros.

P(x) = x4+ 16x²-225, 5i is a zero.

Answer 1

• remaining zeros : -5i , 3 , -3

Step-by-step explanation :

• P(x) = x⁴ + 16x² - 225 = 0
• u² + 16u - 225 = 0 [Substitute u = x² to rewrite equation]
• u = 9 or u = -25
• 
  `\therefore` x² = 9 , x = 3 or - 3
• x² = -25 , x = 3i or -3i [Calculation on]
• remaining zeros : -5i , 3 , -3 Ans.