16
mx²+(m-1)x+m=0有实根
判别式△=(m-1)²-4m*m=-3m²-2m+1=-(m+1)(3m-1)≥0
-1≤m≤1/3
17
y=ax²+bx+c
顶点(1/2,25）
可以写作y=a(x-1/2)²+25=ax²-ax+a/4+25
与x轴交于两点,则方程a(x-1/2)²+25=0有解,a＜0
韦达定理x1+x2=1,x1x2=(a+100)/(4a)
横坐标立方和=19
x1³+x2³=(x1+x2)³-3x1x2(x1+x2) = 1³-3*(a+100)/(4a)*1 = 19
3*(a+100)/(4a)=-18
(a+100)/(4a)=-6
a+100=-24a
-25a=100
a=-4
y=-4²+x+24