Given that the parabola y = X2 - (k-1) x-3k-2 intersects the X axis at two points a (α, 0), B (β, 0), and α 2 + β 2 = 17, the value of K is obtained

Given that the parabola y = X2 - (k-1) x-3k-2 intersects the X axis at two points a (α, 0), B (β, 0), and α 2 + β 2 = 17, the value of K is obtained

∵ the parabola and X-axis intersect at two points, ∵ = [- (k-1)] 2-4 (- 3K-2) = K2 + 10K + 9 ＞ 0. ① from the problem, we know that two of the equations X2 - (k-1) x-3k-2 = 0 are α, β. From WIDA's theorem: α + β = k-1, α· β = - 3K-2, α 2 + β 2 = (α + β) 2-2, α β = (k-1) 2-2 (- 3K-2) = 17

It is known that the parabola y = x2 + 4x-k-1 has two intersections with the X axis, and the two focuses are on both sides of the straight line x = 1, so we can find the value range of K!

Y = x & # - 178; + 4x-k-1 = (x + 2) &# - 178; - (K + 5) visible parabola y = x & # - 178; + 4x-k-1 takes the straight line x = - 2 as the axis of symmetry, and the vertex of the image is (- 2, - K-5) because the parabola y = x & # - 178; + 4x-k-1 has two intersections with the X axis, so the vertex (- 2, - K-5) is below the X axis, so - k-5-5 because the parabola y