How do you find a polynomial function that has zeros 0, 2, 5? Precalculus Polynomial Functions of Higher Degree Zeros 1 Answer Alan N. Feb 10, 2017 #f(x)=x^3-7x^2+10x# Explanation: Let #f(x)# be the required polynomial. We are told that #f(x)=0# for #x={0, 2, 5}# Thus: #x, (x-2), (x-5)# must be factors of #f(x)# #:. f(x) = x(x-2)(x-5)# #= x(x^2-7x+10)# #=x^3-7x^2+10x# 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 6711 views around the world You can reuse this answer Creative Commons License