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A cubic function y has real coefficients, and its zeros are 4, 5 and 1. If x=−3, =−448 satisfies its equation, find the equation of the  cubic function in standard form. 

Let the leading coefficient be a if necessary.

 

Please help!

 Jan 28, 2021
 #1
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We  have  that

 

y    =  a  (  x -1) ( x - 4)  ( x - 5)

 

And when x= -3,   y  =  -448      so  we  have

 

-448 = a  ( -3 -1) ( -3 - 4)  ( -3 - 5)

 

-448  =  a ( -4) (-7) (-8)

 

-448  = a ( -224)

 

a =  -448/  -224     =  2

 

So   the  polynomial is

 

y =  2  ( x - 1) ( x - 4) (x - 5)  

 

y = 2  ( x^2 - 5x + 4)  ( x  -5)  

 

y = 2  ( x^3 - 5x^2 + 4x  - 5x^2 + 25x - 20)

 

y =  2 ( x^3 - 10x^2 + 29x -20)

 

y = 2x^3  -  20 x^2  + 58x   - 40

 

 

cool cool cool

 Jan 28, 2021
 #2
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thank u so much u are the best person literally ever thank you have a great life

Guest Jan 28, 2021
 #3
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Well.....thanks!!!.....don't know about the "best person ever" part, but I do  what I can  ....

 

 

cool cool cool

CPhill  Jan 28, 2021

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