Final answer:
The real roots of the equation 4x^4 + 31x³ - 4x² - 89x + 22 = 0 are approximately x = -1.4 and x = 0.1.
Step-by-step explanation:
To identify the real roots of the equation 4x4 + 31x³ - 4x² - 89x + 22 = 0, we can use various methods such as factoring or using the rational roots theorem. However, in this case, factoring may be difficult, so we can use a graphing calculator or software to find the real roots. By graphing the equation, we can find that the real roots are approximately x = -1.4 and x = 0.1.