Find all the zeros ofthe function and write the polynomial as a product of linear factors: f(x)=5x^3-9x^2+28x=6

Talon Mcbride 2022-07-28 Answered
Find all the zeros ofthe function and write the polynomial as a product of linear factors:
f ( x ) = 5 x 3 9 x 2 + 28 x = 6
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Answers (1)

Caylee Davenport
Answered 2022-07-29 Author has 14 answers
f ( x ) = 5 x 3 9 x 2 + 28 x + 6
if x=-1/5 is a root of f(x) then f(-1/5) =0.
f ( 1 / 5 ) = 5 ( 1 5 ) 3 9 ( 1 5 ) 2 + 28 ( 1 5 ) + 6 = 0
( 5 x 3 9 x 2 + 28 x + 6 ) ÷ ( x + 1 / 5 ) = 30 10 x + 5 x 2
30 10 x + 5 x 2 = 0 ( x ( 1 i 5 ) ) ( x ( 1 + i 5 ) ) = 0
5 x 3 9 x 2 + 28 x + 6 = ( x + 1 / 5 ) ( x ( 1 i 5 ) ) ( x ( 1 + i 5 ) ) = 0
Hence
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