Question

Find a quartic function with the given x -values as its only real zeros. x=4 and x=2 .

Answer 1

`f(x) = \alpha (x - 4) {}^(2) (x - 2) {}^(2) \\ f(x) = \alpha (x {}^(2) - 8x +16 )(x - 4x - 4) \\ f(x) = \alpha (x {}^(4) - 12x {}^(3) + 52x {}^(2) - 96 x + 64) \\ where \: \alpha ∈ \: \real`