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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 $f(x) + b\cdot g(x)$?

 

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 $f(x) + b\cdot g(x)$?

 Mar 26, 2020
 #1
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Note  that if we  multiply  g(x)  by  -(1/2)  we get   -x^4 + 3x^2 -x + 1/2

Adding this  to  f(x) produces  -x + 5/2

So....the  smallest  possible  degree of  f(x) + b * g(x)   =    1

 

 

cool cool cool

 Mar 26, 2020

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