F4 Math - Quadratic Equations

圖片參考：http://img831.imageshack.us/img831/6954/ch1b.png


1) When x = m ,

LHS = m^2 + 3lm
RHS = m(3l + m) = m^2 + 3lm = RHS

So m is a root , product of the roots = 3lm ,

the other root = 3lm / m = 3l


2)

Let two roots be A and A - 5 ,

Sum of the roots :

A + A - 5 = - (-2k)/2

2A - 5 = k

A = (5+k)/2


Product of the roots :

A(A-5) = (3k+1)/2

[(5+k)/2] [(5+k)/2 - 5] = (3k+1)/2

(k+5)(k+5 - 10) = 2(3k+1)

(k+5)(k-5) = 6k + 2

k^2 - 25 = 6k + 2

k^2 - 6k - 27 = 0

(k + 3)(k - 9) = 0

k = - 3 or k = 9