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part a

Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^4 - 6x^2 +2x - 1. Let a be a constant. What is the largest possible degree of f(x) + a * g(x)?

part b

Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^4 - 6x^2 +2x - 1. Let b be a constant. What is the smallest possible degree of the polynomial f(x) + b * g(x)?

 

Thank youu!

 Mar 24, 2019
 #1
avatar+102355 
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a)  multiplying g   by  a constant other than -1/2  will  not change the degree of  f(x) + a* g(x)

Its degree will still  be 4

 

b)  multiplying g by -1/2   will result  in     -x^4 + 3x^2 - x  + 1/2

When added to   f(x)   we get    -x +   5/2    ⇒    degree 1

 

 

cool cool cool

 Mar 24, 2019
 #2
avatar+533 
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Those questions are from here I think: https://web2.0calc.com/questions/please-help-functions-and-graphing

 Mar 24, 2019

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