急~有數學唔識做？？

1.考慮函數f(x)=x2次方+bx-15,其中b為一常數,已知y=f(x)的圖像通過點(4,9)。
a)求b。由此,或利用其他方法,求y=f(x)的圖像的兩個x軸截距。
Since f(x) passes through (4,9),
9 = 16 + 4b - 15
9 = 1 + 4b
4b = 8
b = 2
Sum of roots = -2 , Product of roots = -15
Let roots be m and n,
(m-n)^2 = m^2 - 2mn + n^2
= m^2 + 2mn + n^2 - 4mn
= (m+n)^2 - 4mn
= 4 + 60
= 64
Distance of two roots
= |m - n|
= sqrt 64
= 8
b)設k為常數。若方程f(x)=k有兩個相異實根,求k的取值範圍。
f(x) = k has two distinct roots,
x^2 + 2x - 15 - k = 0 has two distinct real roots,
△ > 0
4 + 4(15+k) > 0
4 + 60 + k >0
k > -64
2.設f(x)=(x-a)(x-b)(x+1)-3,其中a及b均為正整數且a<b。已知f(1)=1。
a)證明(a-1)(b-1)=2
Given f(1) = 1,
1 = (1-a)(1-b)(1+1) - 3
4 = 2(a-1)(b-1)
(a-1)(b-1) = 2
b)寫出a及b的值
(a-1)(b-1) = 2, since a,b >= 1, (a-1)(b-1) >0,
(a-1),(b-1) >0
For 2, the factor of 2 is 1,2,
Since a >b, a-1>b-1
a-1 = 2, b-1 = 1,
a = 3, b = 2
多項式
3.已知x+1是x3次方-x2次方-3x-1的因式。由此,解x3次方-x2次方-3x-1=0
Let f(x) be x^3 - x^2 - 3x - 1,
Given f(-1) = 0,
x^3 - x^2 - 3x - 1 = 0
(x+1)(x^2 - 2x - 1) = 0