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?
2026-04-30 08:36:50.1777538210
Line does not intersect with curve
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\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}