Question

F(x)=a(x-1)(x-2);g(x)=x+2)(x-2) dan h(x)=c(x+2)(x-1).
jikaf(x)+h(x)+g(x)=x^2-5x-2
maka nilai c?

Answer 1

F(x)+h(x)+g(x)= x^2-5x-2
a(x^2-3x+2)+x^2-4+c(x^2+x-2)= x^2-5x-2
ax^2-3ax+2a+x^2-4+cx^2+cx-2c= x^2-5x-2
(a+1+c)x^2+(-3a+c)x+(2a-4-2c)= x^2-5x-2
koefisien x^2 -> a+1+c= 1-> a+c= 0 -> a= -c
koefisien x -> -3a+c= -5 -> 4c= -5 -> c= -5/4
konstanta -> 2a-4-2c= -2-> -4c= 2 -> c= -1/2