Write an equation in standard form of a polynomial with real

Write an equation in standard form of a polynomial with real coefficients that has roots 1,4i, and -2-2i, that passes through the point (0,-68)?

Solution

Ans:: The equation in standard form of a polynomial with real coefficients that has roots 1,4i, and -2-2i

f(x) = k(x-1)(x-4i)(x-(-2-2i))

f(x) = k(x-1)(x-4i)(x+2+2i)

f(x) Passes through the point (0,-68) hence f(0) =-68

f(x) = k(x-1)(x-4i)(x+2+2i)

f(0) = k(0-1)(0-4i)(0+2+2i)=-68

8k = 68/(1-i)

8k = 34(1+i)

k= 4.25(1+i)

f(x) = 4.25(1+i)(x-1)(x-4i)(x+2+2i)