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

Hayley Steele

Hayley Steele

Answered question

2023-02-19

How to find all zeros of f ( x ) = x 4 - x 3 - 20 x 2 ?

Answer & Explanation

davz198888za

davz198888za

Beginner2023-02-20Added 9 answers

We have solution:
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
f ( x ) = x 2 ( x - 5 ) ( x + 4 )
to find zeros set f ( x ) = 0
x 2 ( x - 5 ) ( x + 4 ) = 0
equate each factor to zero and solve for x
x 2 = 0 x = 0 with multiplicity 2
x - 5 = 0 x = 5
x + 4 = 0 x = - 4

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