Question 1030215: find cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 5, -2, -24 respectively.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Let these be the roots: p, r, v.
The description is this system:
This is not a linear system, and solving it may take many steps. I have not gone further.
Answer by ikleyn(52777)  (Show Source):
You can put this solution on YOUR website! .
find cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 5, -2, -24 respectively.
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Let this polynomial be
p(x) =  =  ,
and  ,  and  are its roots.
Then, as you can check by performing multiplication and opening the parentheses,
a =  = -5,
b =  = -2,
c =  = 24.
So, the polynomial is p(x) =  .
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