kes1968

another question , another superb explanation from mod

Melody you are simply awesome ! thanks for the helping mate

so whats the final answer so that i can challenge the answer key?

brother do you really believe its option 4 or just to keep my heart , please clarify if you still believe the answer is 1 , if yes then please prove the same to me as well

brother , if you see your second answer and change it in terms of x , wont you get option 2 and option 4 , 

brother so what you feel (as a math expert) should be the right answer to the given question ,

brother what you have found is the same function just in terms y , but inverse function is symmetrical about y=x axis ,

also f(f^-1(x))=x which is not satisfied , 

by the way if i do the same operation and interchange x and y i get 2 and 4 option , that satifies both conditions

ignoring dollar sign glitch, 

your polynomials is -2[(x-(3+root5)(x-(3-root5)]

simplyfing  

p(x)=-2(x^2-6x+4)

vertex coordinates are (-b/2a, -d/4a)

so vertex is V(3,10)

CALCUALTION :  X = -b/2a=-(-6)/2=3

                             Y=   -D/4a=-(20)/2=10

for (x+1) and (x+2) be a factor of given polynomialp(x) , they must be its roots. and 

hence according to remainder theorem p(-1) and p(-2) must be 0,

so p(-1)=-1-a+b-8=0

     p(-2)=-8-4a+2b-8=0 

solving these 2 simentanous equation.

b-a=9 

b-2a=8

so b= 10 and a is 1

and polynomial becomes x^3-x^2-10x-8=0 

since product of roots is 8(-d/a) and 2 roots are -1 and -2  last root must be 4 so factor is (x-4)

you could also go for long division.!!!

cheers