Answer:
f(x) = 3x^2 - 15x + 12
Explanation:
All of the second degree polynomials listed have a leading coefficient of 3.
Since we are asked which has roots 4 and 1, we know we need to find the polynomial where x is a negative number, then solve for x.
f(x) = 3x^2 - 15x + 12
= 3(x^2 - 5x + 4) --- Here, I factored out the 3.
= 3((x-4)(x-1)) --- solve for the quadratic.
Therefore, solving for x, we have
x - 4 = 0 and x - 1 = 0
x = 4 x = 1
Thus, this polynomial has a lead coefficient of 3 and its roots are 4 and 1.