What are the rational roots of the polynomial f (x) = 20x^4 + x^3 + 8x^2 + x-12

x = 3/4 and x = - 4/5

Step-by-step explanation:

20x⁴ + x³ + 8x² + x - 12

Group:

(20x⁴ + 8x² - 12) + (x³ + x)

Factor:

4 (5x⁴ + 2x² - 3) + x (x² + 1)

4 (5x² - 3) (x² + 1) + x (x² + 1)

(x² + 1) (4 (5x² - 3) + x)

(x² + 1) (20x² + x - 12)

(x² + 1) (4x - 3) (5x + 4)

So the rational roots are x = 3/4 and x = - 4/5.