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

asked Mar 16, 2023 92.5k views

4 votes

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

points.

4.2k points

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2 votes

Answer:

k<1, k>5

Explanation:

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

Schleir answered Mar 20, 2023

3.4k points

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