create a polynomial f with real number coefficients which ha

create a polynomial f with real number coefficients which has all of the desired

characteristics. You may leave the polynomial in factored form.

The zeros of f are c =±1 and c =±i

The leading term of f(x) is 42x4

Solution

The zeros of polynomial are + / -1 and +/- i

f(x) = a(x +1)(x-1)(x+i)(x-i)

= a(x^2 -1)(x^2 +1)

Leading coefficient ax^4 = 42x^4 . So, a = 42

So, f(x) = 42(x^2 -1)(x^2 +1)