rational root theorem

Question

Use the rational root theorem to identify the possible roots. Verify with synthetic division and write as a product of its factors. Use the factors to find the remaining roots. Use additional paper for your work.

f(x)=x^3-2x^2+5x-4

Answer 1

Possible rational zeros: ±1, ±2, ±4.

x = 1 is zero because f(1) = 1 - 2 + 5 - 4 = 0.

1 I 1 -2 5 -4

1 -1 4

1 -1 4 0

Quotients: x² - x + 4 = 0; x = (1 ± √1 -16)/2 = (1 ± i√15)/2