Question

Obtain all zeroes of the polynomial x4 + 2x3 – 25x2 – 26 x + 120, if two of its zeroes are 2 and 4.

Answer 1

Answer:

x=-5, 2, 4, -3

Step-by-step explanation:

Factor and you get:

(x−2)(x+3)(x−4)(x+5)

Answer 2

Answer:  the zeros are x = {-5, -3, 2, 4}

Step-by-step explanation:

x⁴ + 2x³ - 25x² - 26x + 120 = 0

Given: x = 2 and x = 4

Use synthetic division to find the reduced polynomial for x = 2 and then x = 4

2 |  1     2     -25     -26     120    

  |  ↓    2        8     -34     -120

     1    4      -17      -60      0  ← remainder

4 |  1    4      -17      -60

  |  ↓   4      32        60

     1    8      15         0  ←  remainder

      1x² + 8x + 15 = 0

      (x + 5) (x + 3) = 0

      x + 5 = 0    x + 3 = 0

        x = -5            x = -3

The zeros are: x = 2, x = 4, x = -5, and x = -3