How do you find all zeros of #f(x)=x^4-x^3-20x^2#?

1 Answer
Dec 12, 2017

Answer:

#x=-4,x=0,x=5#

Explanation:

#"take out a common factor of "x^2#

#f(x)=x^2(x^2-x-20)#

#"the factors of - 20 which sum to - 1 are - 5 and + 4"#

#rArrf(x)=x^2(x-5)(x+4)#

#"to find zeros set "f(x)=0#

#rArrx^2(x-5)(x+4)=0#

#"equate each factor to zero and solve for x"#

#x^2=0rArrx=0" with multiplicity 2"#

#x-5=0rArrx=5#

#x+4=0rArrx=-4#