How do you write a polynomial with zeros: 2i, sqrt2, and 2? Precalculus Polynomial Functions of Higher Degree Zeros 1 Answer Shwetank Mauria Mar 9, 2016 #x^3-(2+sqrt2+2i)x^2+(2sqrt2+(2sqrt2+4)i)x-4sqrt2i# Explanation: The polynomial with zeros: #2i,sqrt2# and #2# is #(x-sqrt2)(x-2)(x-2i)# or #(x^2-sqrt2x-2x+2sqrt2)(x-2i)# or #(x^3-sqrt2x^2-2x^2+2sqrt2x-2ix^2+2sqrt2ix+4ix-4sqrt2i)# or #x^3-(2+sqrt2+2i)x^2+(2sqrt2+(2sqrt2+4)i)x-4sqrt2i# 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 1253 views around the world You can reuse this answer Creative Commons License