



 
Hi Roxanne, I always draw pictures. Here is my picture of a line and a curve and a line where the line cuts the curve. I let $(a,b)$ be the point where the line cuts the curve. Since $(a,b)$ lies on the line it satisfies the equation of the line and hence \[b = 2a  5.\] The point $(a,b)$ is also on the curve so \[b = a^2 + ka + 11.\] Hence \[2a  5 = a^2 + ka + 11.\] For what range of values of $k$ does the quadratic above have real roots? Penny  


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