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Find a degree 4 polynomial having zeros -5, -2, 4 and 8 and the coefficient of 24 equal 1.The polynomial is

Find a degree 4 polynomial having zeros -5, -2, 4 and 8 and the coefficient of 24 equal-example-1
User Razpeitia
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x^4-5x^3-42x^2+104x+320=0

1) We are going to start with the factored form of a function. Given by this formula for a 4th-degree function:


y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)

In this question, the leading coefficient has been given to us already, so we can plug into that a=1


y=1(x-x_1)(x-x_2)(x-x_3)(x-x_4)

2) Now let's plug into them the other roots:


y=(x+5_{})(x+2_{})(x-4_{})(x-8_{})

2.2) Let's rewrite that function as an equation plugging y=0, and expanding it:


\begin{gathered} (x+5_{})(x+2_{})(x-4_{})(x-8_{})=0 \\ x^4-5x^3-42x^2+104x+320=0 \end{gathered}

And that is the answer

User GSD
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