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The degree of the polynomial function f(x) is 4.
The roots of the equation f(x) = 0 are -8, -5.1. and 2
Which graph could be the graph

Answer :

See the graph below

Explanation:

A polynomial function whose degree is 4 is given by the form:

[tex]f(x)=ax^4+bx^3+cx^2+dx+e \\ \\ Or: \\ \\ f(x)=a(x-x_{1})(x-x_{2})(x-x_{3})(x-x_{4}) \\ \\ \\ Where: \\ \\ x_{1},x_{2},x_{3} \ and \ x_{4} \ are \ the \ roots[/tex]

Here the roots are:

[tex]x_{1}=-8 \\ \\ x_{2}=-5 \\ \\ x_{3}=1 \\ \\ x_{4}=2[/tex]

If we set [tex]a=1[/tex] then:

[tex]f(x)=(x+8)(x+5)(x-1)(x-2)[/tex]

Finally, by using graphing tool we get the graph of our polynomial function:

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