Question

Set up an equation of a tangent to the graph of the following function.
Find the value of the coefficient k for which the curve $y=x^2+kx+4$ touches the Ox axis.

Answer 1

The parabola $x^2+kx+4=0$ touches the x-axis .It means $y=0$ is a tangent to the given parabola.

$\frac{dy}{dx}=2x+k=0\Rightarrow x=-\frac{k}{2}$

Put $y=0,x=-\frac{k}{2}$ in the equation of given parabola

$0=\frac{k^2}{4}-\frac{k}{2}+4$

$k=\pm 4$