Question

For the function f(x) = 3x^2 - 16x + 48, what are the possible rational zeros?

a) -4, -2, 2, 4
b) -6, -3, 3, 6
c) -8, -4, 4, 8
d) -12, -6, 6, 12

Answer 1

The possible rational zeros for the given function f(x) = 3x^2 - 16x + 48 are x = 4 and x = 8.

Step-by-step explanation:

The given function is f(x) = 3x^2 - 16x + 48. To find the possible rational zeros, we can use the Rational Root Theorem. The possible rational zeros are of the form p/q, where p divides the constant term (48 in this case) and q divides the leading coefficient (3 in this case).

So, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

After trying out the different possible rational zeros, we find that the rational zeros for the function f(x) = 3x^2 - 16x + 48 are x = 4 and x = 8.