Question 1030215
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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) = {{{x^3 + ax^2 + bx + c}}} = {{{(x-x[1])*(x-x[2])*(x-x[3])}}},

and {{{x[1]}}}, {{{x[2]}}} and {{{x[3]}}} are its roots.


Then, as you can check by performing multiplication and opening the parentheses,

a = {{{-(x[1] + x[2] + x[3])}}} = -5,

b = {{{x[1]*x[2] + x[1]*x[3] + x[2]*x[3]}}} = -2,

c = {{{-x[1]*x[2]*x[3]}}} = 24.

So, the polynomial is p(x) = {{{x^3 - 5x^2  - 2x + 24}}}.
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