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kx - 4 = x^2 - 2x2 Find the set of values of k for which the line y = kx − 4 intersects the curve y = x2 − 2x at two distinct points. [4]
From s09p1.
I get we have to equate the answer and then use the discriminant but after getting 2 and -6 how do you know what each inequality we need to put?
Like the answer is k>2 and k<-6
How do we get this part right?
x^2 - 2x - kx + 4 = 0
x^2 - x (2 + k) + 4 = 0
Use b^2-4ac = 0 (Discriminant = 0 as curve intersects at two distinct points)
k^2 + 4k + 4 - 16 = 0
hence, k > 2 and k < -6