f.4 math help!¬^^

let P(x)= x^3 + 4x^2 - 30x - 8

(a)find P(4)

(b)slove p(x)=0
(a)
P(4)
=4^3+4(4^2)-30(4)-8
=64+64-120-8
=0
(b)
P(x)=0
(x-4)(x^2+8x+2)=0
x-4=0 or x^2+8x+2=0
when x-4=0
x=4
when x^2+8x+2=0
x=1/2[-8+√(64-8)] or x=1/2[-8-√(64-8)]
x=1/2[-8+√(58)] or x=1/2[-8-√(58)]

2007-01-28 23:50:25 補充：
since P(4)=0 . 4 is a root of P(x) or(x-4) is a factor of P(x)

2007-01-29 00:46:32 補充：
最後個step做錯添x=1/2[-8+√(56)] or x=1/2[-8-√(56)]x=-4+√14 or x=-4-√14不過今回我唔會為了做錯少少delete架啦。

正確ANS.:
P(4)

=4^3+4(4^2)-30(4)-8

=64+64-120-8

=0

(b) Since P(4) = 0, by factor thm,,
(x-4) is a factor of P(x)

So P(x) can be written as
P(x) = x³ + 4x² - 30x - 8 = (x-4)(x² + ax + b) identically
= x³ + (-4 + a)x² + (-4a + b)x - 4b

So,
-4+a = 4..........(1)
-4b = -8..........(2)

Solving (1) and (2), a = 8, b = 2

P(x) = (x-4)(x²+8x+2) = 0

x-4 = 0 or x²+8x+2 = 0

x = 4 or x = 1/2*[-8 ± sqrt(8²-4*2)]
x = 4 or x = 1/2*[-8 ± sqrt(56)]
x = 4 or x = 1/2*[-8 ± 2sqrt(14)]
x = 4 or x = -4 ± sqrt(14)
x = 4, -0.258 or -7.74

2007-02-09 09:21:07 補充：
good ans.

P(x) = x³ + 4x² - 30x - 8
(a) P(4)
= 4³ + 4*4² - 30*4 - 8
= 64 + 64 - 120 - 8
= 0

(b) Since P(4) = 0, by factor theorem,
(x-4) is a factor of P(x)

So P(x) can be written as
P(x) = x³ + 4x² - 30x - 8 = (x-4)(x² + ax + b) identically
= x³ + (-4 + a)x² + (-4a + b)x - 4b
So,
-4+a = 4..........(1)
-4b = -8..........(2)
Solving (1) and (2), a = 8, b = 2
P(x) = (x-4)(x²+8x+2) = 0
x-4 = 0 or x²+8x+2 = 0
x = 4 or x = 1/2*[-8 ± sqrt(8²-4*2)]
x = 4 or x = 1/2*[-8 ± sqrt(56)]
x = 4 or x = 1/2*[-8 ± 2sqrt(14)]
x = 4 or x = -4 ± sqrt(14)
x = 4, -0.258 or -7.74