Question

Question

Answer 1

The given polynomial is f(x) = $\left(k-1\right)x^2+kx+1$.
Since $-3$ is one of the zeroes of the given polynomial, so $f\left(-3\right)=0$.
$$\begin{gathered} \left(k-1\right){\left(-3\right)}^2+k\left(-3\right)+1=0 \\ \Rightarrow 9\left(k-1\right)-3k+1=0 \\ \Rightarrow 9k-9-3k+1=0 \\ \Rightarrow 6k-8=0 \\ \Rightarrow k=\frac{4}{3} \end{gathered}$$
Hence, the correct answer is option A.