Question

Using the rational root theorem, state all the possible roots for the function f(x)=2x^2 −3x+1, solve the function using synthetic division to check and find the actual roots of the function.

a. Possible roots: ±1,±2,±3 Actual roots: x=1 or x =−2
b. Possible roots: ±1, ±1/3 Actual roots: x=−1 or x=1/3
c. Possible roots: ±2, ±1 Actual roots: x=−1 or x=2
d. Possible roots: ±1/2, ±1 Actual roots: x=−1 or x=−1/2

Answer 1

The possible roots are ±1,±2 and the actual roots are x=1 or x =−2

Step-by-step explanation:

The rational root theorem states that if a polynomial equation with integer coefficients has a rational root p/q, then p is a factor of the constant term and q is a factor of the leading coefficient. For the function f(x) = 2x^2 - 3x + 1, the constant term is 1 and the leading coefficient is 2. Therefore, the possible rational roots are obtained by taking the factors of 1 (±1) and dividing them by the factors of 2 (±1, ±2).

Using synthetic division, we can check if any of the possible roots are actual roots of the function. By dividing the function by the possible roots, we find that x = 1 and x = -2 are the actual roots of the function. Therefore, the correct answer is a. Possible roots: ±1,±2. Actual roots: x=1 or x =−2.