Form 4 maths...help

kai cheung

2006-12-05 8:25 am

Let f(x)= ax^2+bx+c, where a is not equal to 0.
(A) If x+2 is a fator of f(x), use the fator theorem
to find, in terms of a and b, a quadratic funtion h
(x) which is divisible by
(i)x-1
(ii)x
(b) If 2x+3 is a fator of f(x+3), find a linear factor
of
(i) f(x),
(ii) f(2x).

回答 (1)

貓朋

2006-12-05 10:06 am

✔ 最佳答案

(a) x+2 is a factor implies f(-2)=0
(i) x-1 is a factor implies h(1)=0
Now, let f(x+k)=h(x) , we should have -2=1+k and hence k= -3 and hence
h(x) = f(x-3) = a(x-3)^2 + b(x-3) +c = .................
(ii) x is a factor implies h(0)=0
Now, let f(x+k)=h(x) , we should have -2=0+k and hence k= -2 and hence
h(x) = f(x-2) = a(x-2)^2 + b(x-2) +c = .................

(b) 2x+3 is a factor implies f( {-3/2} +3) =f(3/2) =0 , then
(i) x- 3/2 is a linear factor of f(x)
(ii) 0= f(3/2) = f( 2x {3/4} ) and hence x- 3/4 is a linear factor of f(2x)

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