Question

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

Answer 1

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.