how to do it (2)

y = 2(x^2) +3x+k ------------------------(1)
4x-y=2---------------------------------------(2)

將(2)寫成 4x-2=y------------------------(3)

把(3)的 y 代入 (1)的 y ，得出﹕4x-2=2(x^2) +3x+k

移項得出﹕2(x^2) - x+(k+2)=0---------(4)

因為此聯立方程只有一個解，而且一定是實數解 (因為複數解一定最少有兩個)

所以(4)的判別式(discriminant)一定等於零

(4)的判別式 = (-1^2)-4(2)(k+2) = 0 -----(5)

解方程(5)便能求出所需的k﹕
k=0.125 - 2 = -1.875

把k值代入(4)，再解方程
2(x^2) - x+(k+2)=0---------(4)
2(x^2) - x+(0.125)=0---------(4)

化簡後得出﹕
16(x^2)-8x+1=0
(4x-1)^2 = 0
所以 4x-1 = 0，x=0.25 (重根, double roots)

最後把x值代入(3)
4x-2=y------------------------(3)
4(0.25) -2 = y

y = -1 (重根)

===========================
答案﹕
k = -1.875
x=0.25, y=-1 (一對二重根)

希望幫到你=)

ｙ＝２ｘ＾２＋３ｘ＋ｋ
４ｘ－ｙ＝２

y = 4x - 2
4x - 2 = 2x^2 + 3x + k
2x^2 - x + (k+2) = 0

to have equal root , delta = 0
(-1)^2 - 4(2)(k+2) = 0
1- 8k - 16 = 0
k = -15/8