How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 4, -1, -3i? Precalculus Polynomial Functions of Higher Degree Zeros 1 Answer Vinícius Ferraz May 26, 2017 #p(z) = z^4 - 3z^3 + 5z^2 - 27z -36# Explanation: #p(z) = (z - 4)(z + 1)(z - 3i)(z + 3i)# #= (z^2 -3z - 4)(z^2 + 9)# #= z^4 - 3z^3 -4z^2 + 9z^2 - 27z -36# Answer link Related questions What is a zero of a function? How do I find the real zeros of a function? How do I find the real zeros of a function on a calculator? What do the zeros of a function represent? What are the zeros of #f(x) = 5x^7 − x + 216#? What are the zeros of #f(x)= −4x^5 + 3#? How many times does #f(x)= 6x^11 - 3x^5 + 2# intersect the x-axis? What are the real zeros of #f(x) = 3x^6 + 1#? How do you find the roots for #4x^4-26x^3+50x^2-52x+84=0#? What are the intercepts for the graphs of the equation #y=(x^2-49)/(7x^4)#? See all questions in Zeros Impact of this question 2507 views around the world You can reuse this answer Creative Commons License