Let $\alpha,$ $\beta,$ $\gamma,$ and $\delta$ be the roots of
\[x^4 + kx^2 + 90x - 2009 = 0.\]If $\alpha \beta = 49,$ find $k.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\alpha,$ $\beta,$ $\gamma,$ and $\delta$ be the roots of
\[x^4 + kx^2 + 90x - 2009 = 0.\]If $\alpha \beta = 49,$ find $k.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
7
Let $\alpha,$ $\beta,$ $\gamma,$ and $\delta$ be the roots of
\[x^4 + kx^2 + 90x - 2009 = 0.\]If $\alpha \beta = 49,$ find $k.$
train