maths~~~~~~

若 y = x² + (k+1)x + 4 的圖像與x軸只接解一點,
(a)求k的值;
y = x² + (k+1)x + 4 = 0
判別式 = (k+1)^2 - 16 = 0
k+1 = 4 or k+1 = -4
k = 3 or k = -5

(b)從而求每個k值所對應的x軸截距。
when k = 3,
x² + 4x + 4 = 0
(x + 2)^2 = 0
x = -2
截距 = 2
when k = -5,
x² - 4x + 4 = 0
(x - 2)^2 = 0
x = 2
截距 = 2

a/
Δ=b^2 -4ac =0
(k+1)^2 -4(4)=0
k^2 +2k +1 -16=0
k^2 +2k -15 =0
(k-3)(k+5)=0
k = 3 or -5

b/
y=x²+(k+1)x+4=0

k=3,
x²+(3+1)x+4=0
x²+4x+4=0
(x+2)^2 =0
x = -2

k= -5,
x²+( -5+1)x+4=0
x² -4x+4=0
(x -2)^2 =0
x = 2