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I need help and I'm not sure how to solve it

I need help and I'm not sure how to solve it-example-1
User Fu
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1 Answer

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we know that

g(x)------> has a root of multiplicity 2 at t=2 ------> (t-2)^2

roots of multiplicity 1 at t=0 and t=-3------> t(t+3)(t-2)^2

so

the equation of g(x) is

g(x)=at(t+3)(t-2)^2

where a is the leading coefficient

Remember that

g(5)=288

so

For x=5, g(x)=288

substitute the given values in the equation and solve for a

288=a(5)(5+3)(5-2)^2

288=a(5)(8)(3^2)

288=a(360)

a=288/360

a=0.8

therefore

the answer is

g(x)=0.8t(t+3)(t-2)^2

User Mkurnikov
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