Consider the functions fx x x 3 x 2 fx x3 x2 Find the r

Consider the functions f(x) = (x + )(x + )^3 (x - )^2 f(x) = x^3 x^2 Find the real zeroes of each function and. state the multiplicity of each zero. Find the y-intercept of each function.

Solution

f(x) = x^3 - x^2

=x^2(x -1) = x*x*(x-1)

a) Zeros are found by plugging f(x) =0

So, x*x*(x-1)=0

Zeros are x= 0 (mulitplicty 2)

x = 1 (multiplicity 1)

b) Y intercept : PLug x= 0 in f(x)

f(0) = 0*0(0 -1) =0

So, f(x) passes through origin ( 0, 0)