How do you find all zeros with multiplicities of #f(x)=-17x^3+5x^2+34x-10#? Precalculus Polynomial Functions of Higher Degree Zeros 1 Answer Binayaka C. Jul 14, 2017 The zeros are #x = 5/17 , x = sqrt2 , x = -sqrt 2# Explanation: #f(x) = -17 x^3 +5x ^2 +34x -10 # or #f(x) = -17 x^3 +34x +5x^2 -10 # or #f(x) = -17x( x^2 -2) +5(x^2 -2)# or #f(x) = ( x^2 -2)(-17x+5) # or #f(x) = ( x +sqrt2)(x-sqrt2)(-17x+5) # #f(x)=0 # When #( x +sqrt2)=0 or x = -sqrt 2# , #(x-sqrt2) =0 or x = sqrt2 # and #(-17x+5)=0 or 17x =5 or x = 5/17# The zeros are #x = 5/17 , x = sqrt2 , x = -sqrt 2# [Ans] 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 1572 views around the world You can reuse this answer Creative Commons License