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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 $f(x) + a*g(x)$?

 

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 $f(x) + b*g(x)$?

Guest Aug 7, 2017

Best Answer 

 #1
avatar+26758 
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a.  As long as a is not -1/2 then there will always be a term in x4, so fourth order is the largest possible.

 

b.  If you choose b = -1/2 then the x4 and x2 terms vanish and you are left with a linear expression (I.e. first order).

Alan  Aug 7, 2017
 #1
avatar+26758 
+1
Best Answer

a.  As long as a is not -1/2 then there will always be a term in x4, so fourth order is the largest possible.

 

b.  If you choose b = -1/2 then the x4 and x2 terms vanish and you are left with a linear expression (I.e. first order).

Alan  Aug 7, 2017

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