Using the Rational Root Theorem, state all the possible rational roots for the function. Then, solve the function using synthetic division to check and find the actual roots of the function. f(x)=2x2+3x+1 (1 point) Responses Possible roots: ±2, ±1 Actual roots: x = 1 or x=2 Possible roots: ±2, ±1 Actual roots: x = 1 or x=2 Possible roots: ±1, ±13 Actual roots: x = −1 or x=13 Possible roots: ±1, ±13 Actual roots: x = −1 or x=13 Possible roots: ±12, ±1 Actual roots: x =−1 or x=−12 Possible roots: ±12, ±1 Actual roots: x =−1 or x=−12 Possible roots: ±1, ±2, ±3 Actual roots: x = 1 or x=−2
The possible rational roots for the function f(x) = 2x^2 + 3x + 1 are ±1 and ±2.
Using synthetic division, we can check these possible roots to find the actual roots of the function:
For x = 1:
1 | 2 3 1
2 5 6
The remainder is 6, so x = 1 is not a root.
For x = -1:
-1 | 2 3 1
-2 -1
The remainder is -1, so x = -1 is not a root.
For x = 2:
2 | 2 3 1
4 14
The remainder is 14, so x = 2 is not a root.
Therefore, the actual roots of the function f(x) = 2x^2 + 3x + 1 are x = 1 and x = 2.