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  • 06-11-2019
  • Mathematics
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Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1,given that f(0)=60.

f(x)=

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Аноним Аноним
  • 06-11-2019

Up to multiples, if you're given the roots you can write the polynomial by multiplying several parenthesis in the form

[tex](x-x_0)[/tex]

where [tex]x_0[/tex] is a root. So, in your case, you have

[tex]f(x) = a(x+6)(x+5)(x+1)[/tex]

We can fix the parameter a by imposing f(0)=60:

[tex]f(0)=a(0+6)(0+5)(0+1)=30a=60\iff a=2[/tex]

So, your polynomial is

[tex]f(x) = 2(x+6)(x+5)(x+1)=2x^3+24x^2+82x+60[/tex]

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