SOLUTION: 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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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(52778)   (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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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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