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rianna14
22.10.2019 •
Mathematics
For each cubic function below, one of the zeros is given. express each cubic function in terms of linear factors.a)f(x)=2x³-9x²-53x-24; f(8)=0b)f(x)=x³+x²+6x+6; f(-1)=0
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Ответ:
a)2x³-9x²-53x-24 = (x-8) (2x + 1) ( x +1)
b)x³+x²+6x+6 = ( x +1 ) ( x - i√6) ( x + i√6)
Step-by-step explanation:
a)
f(x)=2x³-9x²-53x-24
f(8)=0
It means that 8 is the root of the function f(x)
2x³-9x²-53x-24 = (x-8)(2 x² + 7 x +3)
Now find the factor of (2 x² + 7 x +3)
2 x² + 7 x +3 = 2 x² + 6 x + x + 3
= 2 x( x + 3)+ 1 (x+3)
= ( 2x + 1) ( x +1)
So
2x³-9x²-53x-24 = (x-8) (2x + 1) ( x +1)
b)
f(x)=x³+x²+6x+6
f(-1)=0
It means that -1 is the root of the function f(x)
x³+x²+6x+6 = ( x +1 )( x² +6)
We know that
a² - b² =(a+b)(a-b)
i² = - 1
So
x² +6 = ( x - i√6) ( x + i√6)
x³+x²+6x+6 = ( x +1 )( x² +6)
x³+x²+6x+6 = ( x +1 ) ( x - i√6) ( x + i√6)
Ответ:
XD well lad um yes i have before, but why is this a Question? :)
Step-by-step explanation: