Find the values of k such that 3 is a zero of f(x)= x^3+x^2+kx+1

Question

I tried to compute f(3) and got k =-37/3 but the answer in the textbook is k = -2 root(3) k=2 root(3)

Answer 1

Set f(3)=0 and solve for k.

f(3) = 3³ + 3² + 3k + 1 = 0 ⇒

k = (- 27 - 9 - 1) / 3 = -37/3

I agree with your answer.