How to find the zeros of f(x) = x^3 − 5x^2 − 3x + 15?

datgeni5quc

datgeni5quc

Answered question

2023-02-17

How to find the zeros of f ( x ) = x 3 5 x 2 3 x + 15 ?

Answer & Explanation

Caltolmsn

Caltolmsn

Beginner2023-02-18Added 9 answers

f ( x ) = x 3 - 5 x 2 - 3 x + 15
Notice how the ratio between the first and second phrases and the third and fourth terms are the same.
Due of the grouping, this cubic will factor:
x 3 - 5 x 2 - 3 x + 15
= ( x 3 - 5 x 2 ) - ( 3 x - 15 )
= x 2 ( x - 5 ) - 3 ( x - 5 )
= ( x 2 - 3 ) ( x - 5 )
= ( x - 3 ) ( x + 3 ) ( x - 5 )
Therefore zeros:
± 3 and 5

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