The equation of a curve is $$\(y=2 x^{2}+k x+k-1\)$$, where $$\(k\)$$ is a constant. Given that the line $$\(y=2 x+3\)$$ is a tangent to the curve, find the value of $$\(k\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_12 Year：2020 Question No：6(a)
Answer:
\[
2 x^{2}+k x+k-1=2 x+3 \rightarrow 2 x^{2}+(k-2) x+k-4=0
\]
Use of \(b^{2}-4 a c=0 \rightarrow(k-2)^{2}=8(k-4)\)
\[
k=6
\]
2 x^{2}+k x+k-1=2 x+3 \rightarrow 2 x^{2}+(k-2) x+k-4=0
\]
Use of \(b^{2}-4 a c=0 \rightarrow(k-2)^{2}=8(k-4)\)
\[
k=6
\]
Knowledge points:
1.3.5 understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations. (e.g. to determine the set of values of for which the line intersects, touches or does not meet a quadratic curve.)
Solution:
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