the line $y=kx+1$ does not intersect with the graph of $y = x^2-3x+5$ at any points
Find the range of possible values for $k$?
Can anyone help?
the line $y=kx+1$ does not intersect with the graph of $y = x^2-3x+5$ at any points
Find the range of possible values for $k$?
Can anyone help?
\begin{align} kx+1&=x^2-3x+5\\ 0&=x^2-3x-kx+5-1\\ x^2-(3+k)x+4&=0\\ x=\dfrac{(3+k)\pm\sqrt{(3+k)^2-16}}{2}\\ \text{For No Intersection,}\\ (3+k)^2-16<0\\ (3+k)^2<16\\ -4<(3+k)<4\\ -7< k <1\\ \end{align}