Question

Find the root of
x
3−2x2−5x+6=0
A. 1, 2, -3
B. -1, 2, 3
C. 1, 2, 3
D. 1, -2, 3

Answer 1

To find the roots of the equation x^3 - 2x^2 - 5x + 6 = 0, we can use synthetic division or factor it using the rational root theorem.

Using synthetic division, we can test each of the answer choices to see which one is a root. Let's try option C, which is 1, 2, and 3.

For x = 1:
1 | 1 - 2 - 5 + 6
1 - 1 - 6
- 6

The result is not zero, so 1 is not a root.

For x = 2:
2 | 1 - 2 - 5 + 6
2 0 - 10
- 4

The result is not zero, so 2 is not a root.

For x = 3:
3 | 1 - 2 - 5 + 6
3 3 - 6
0

The result is zero, so 3 is one root of the equation.

Therefore, the correct answer is D. 1, -2, 3.