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Find the value of k such that the equation of the tangent line to f(x) = x^2 + k*x is equal to y = 5*x + 3

1 Answer

3 votes
The equation
x^2+kx=5x+3 must have only one solution for the line
y to be a tangent line to the quadratic function
f(x).


x^2+kx=5x+3\\ x^2+kx-5x-3=0\\ x^2+(k-5)x-3=0\\ \Delta=(k-5)^2-4\cdot1\cdot(-3)=(k-5)^2+12\\\\ (k-5)^2+12=0\\ (k-5)^2=-12\\ k\in \emptyset

So there isn't such value of k.
User Aswin
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