X^4-28x^3+272x^2-1065^x+1444

Question

Find x

Answer 1

x⁴ - 28x³ + 272x² - 1065x + 1444 = 0.

Synthetic division method:

    4|1   -28   272   -1065    1444

     |0     4    -96       704   -1444

     |_____________________________

      1   -24   176    - 361      0

x⁴ - 28x³ + 272x² - 1065x + 1444 = (x - 4)(x³ + 24x² + 176x - 361) = 0

x - 4 = 0 and (x³ + 24x² + 176x - 361) = 0

The one solutions is x = 4.

The roots of the 3rd degree equation can be approximated using Newton's method, for instance

x₁ = 3.41557

x₂ = 4

x₃ = 9.80592

x₄ = 10.77931.