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| Math Central | Quandaries & Queries |
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Question from Roxanne: Hello, i need to ask a question, do you mind explaining and writing the formula of how to solve equations such as "find the set values of k for which the line y=2x-5 cuts the curve y=x^2 +kx+11" please |
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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