Write a polynomial in standard form of LEAST DEGREE WITH INT

Write a polynomial in standard form of LEAST DEGREE WITH INTEGER COEFFICIENT whose zeros are: x= 0 (multiplicity 2), 4i, and - sqrt(3)

Solution

P(x) = x*x*(x - 4i)*(x + 4i)*(x + sqrt(3))*(x - sqrt(3)) =0

=> x²*(x² + 16)*(x² -3) = 0

=> (x⁴ + 16x²)(x² - 3) = 0

=> x⁶ + 13x⁴ - 48x² = 0