Question

Find all zeros of the polynomial x⁴ - 5x³ - 4x² + 16x - 8, if two of its zeros are 3 + √5 and 3 - √5

Answer 1

Answer:

Since (1 – √5) is a root of the polynomial P(x) = 0 (1 + √5) is also a root of P (x) = 0 ⇒ x2 – [(1 + √5) + (1 – √5)]x + (1 + √5) (1 – √5) = 0 is a factor of P(x) = 0 ⇒ x2 – 2x – 4 = 0 is a factor of P(x) = 0. Dividing the polynomial by x2 – 2x – 4 = 0 We get the other factor x2 – 3x + 2 = 0 The roots of x2 – 3x + 2 = 0 (x – 2) (x – 1) = 0 x = 1, 2 The roots are 1, 2, 1 ± √5

hope it helps

Answer 2

Answer:

roots are 1, -2, 3+√5, 3-√5