Let a and b be real numbers where a=b=0. Which of the following functions could represent the graph below?f(x)=x(x-a)^3(x-b)^3f(x)=(x-a)^2(x-b)^4f(x)=x(x-a)^6(x-b)^2f(x)=(x-a)^5(x-b)

Accepted Solution

Answer:Option: b is the answer. ( f(x)=(x-a)^2(x-b)^4 )Step-by-step explanation:Clearly from the graph of the function we could see that zero is not a root of the polynomial function hence option (a) ( f(x)=x(x-a)^3(x-b)^3 ) and option (c) (  f(x)=x(x-a)^6(x-b)^2 )are discarded.Now we will check for option (b) and option (d)As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.Hence, the correct option is:option: b ( f(x)=(x-a)^2(x-b)^4 ).