Find the rational roots of x^4 + 8x^3 + 7x^2 - 40x - 60 = 0
- 2, 6
- -6, -2
- -2, 6
- -6, 2
To find the rational roots of the given polynomial, we can use the rational root theorem. According to the theorem, the possible rational roots are given by the factors of the constant term (in this case, -60) divided by the factors of the leading coefficient (in this case, 1).
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The factors of 1 are: 1.
Therefore, the possible rational roots are: ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, and ±60.
We can now try these possible rational roots one by one to see which ones satisfy the equation. By doing this, we find that -2 and 6 are both roots of the equation.
Thus, the rational roots of the given polynomial are -2 and 6.
Therefore, the correct answer is: -2, 6.