Answer: D) 4
Step-by-step explanation:
x⁴ - x³ - 9x² + 7x + 14 = 0
possible rational roots are: ±{1, 2, 7, 14}
Try x = -1
-1 | 1 -1 -9 7 14
| ↓ -1 2 7 -14
1 -2 -7 14 0 ← remainder is 0 so x = -1 is a root
Let's try x = 2 with the factored polynomial
2 | 1 -2 -7 14
| ↓ 2 0 -14
1 0 -7 0 ← remainder is 0 so x = 2 is a root
Factored polynomial x² - 7 can be factored to:
(x - √7) (x + √7)
⇒ x = √7 and x = -√7
The roots are x = {-1, 2, √7, -√7) which are all real numbers.
