Find the polynomial function that has the given zeroes; 4, (2+square root of 5), (2-square root of 5)

Question

Looking at given zeroes and writing down the polynomial function from them.

Answer 1

x = 4,     x-4 = 0

x = 2 +√5,      x - 2 - √5 = 0

x = 2 - √5,   x - 2 + √5 = 0

(x-2-√5)(x-2+√5)(x-4) = 0

 

(x² - 4x - 1)(x-4) = 0

x³ - 8x² + 15x + 4 = 0