Real roots: −1/2 , 0, 1/2 and (−2,f(−2))=(−2,6)

Question

Real roots: −1/2 , 0, 1/2 and (−2,f(−2))=(−2,6)

Answer 1

(x+1/2)(x-1/2)x =(x^2-1/4)x = x^3 - x/4

f(-2) = 6

f(-2) =a[ (-2)^3-(-2)/4]= 6

a(-15/2)= 6

a = -12/15 = -4/5

f(x) =(-4/5)(x^3 -x/4)

f(x) = (-4x^3)/5 + x/5