If P(x) is a cubic polynomial such that P(0)=0 P(2)=-4 and P(x)is positive only when x> 4 find P(x)

Jaxon Hamilton 2022-07-31 Answered
If P(x) is a cubic polynomial such that P(0)=0 P(2)=-4 and P(x)is positive only when x> 4 find P(x)
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Answers (2)

phravincegrln2
Answered 2022-08-01 Author has 19 answers
eventually given that numbers greater than 4 would turn out to be positive, P cubed would have to be positive... and you would have to subtract a multiple of P squared... so far the equation would look like P 3 P 2 Now just look for a number that would work there (where _ is) with 2 as a given for P and -4 as the answer... 2 3 = 8 8 ( 2 2 ) = 4 8 ( 4 ) = 4
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Intomathymnma
Answered 2022-08-02 Author has 5 answers
since P(0)=0 and P(x) is positive only when x > 4 then (0,0) must be a double root with the function staying below the x axis.
since P(x) > 0 when x > 4 then a root must exist at x=4
now you have y = a x 2 ( x 4 )
use the given point (2,-4) to find a
4 = a 2 2 ( 2 4 )
-4=a (-8)
a=1/2
therefore cubic polynomial is y = ( 1 / 2 ) x 2 ( x 4 )
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