Find a 4th degree polynomial with integer coefficients that

Find a 4th degree polynomial with integer coefficients that has zeros x = -1, 3, i and has f (0) = 10. You may leave your answer in factored form.

Solution

given coefficients are integers ,-1,3 are roots and i is one root

so its conjugate -i is also the root

polynomial is of the form f(x)=k(x+1)(x-3)(x-i)(x+i)

given f(0)=10

k(0+1)(0-3)(0-i)(0+i) =10

-3k =10

k =-10_/3

f(x)=(-10_/3)(x+1)(x-3)(x-i)(x+i)

f(x)=(-10_/3)(x²-2x-3)(x²+1)

f(x)=(-10_/3)(x⁴-2x³-2x²-2x-3)