Question

4) Find the values of k for which the line y = 3x + 1 cuts the curve y = x² + kx + 2 in two distinct

points.

Answer 1

`k<1, k>5`

Explanation:

`3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5`