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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 $f(x) + b\cdot g(x)$?

 Aug 1, 2022
 #1
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The smallest possible degree is 1.

 Aug 1, 2022
 #2
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Let b = (-1/2)

 

So

 

x^4 - 3x^2 + 2  + (-1/2) [ 2x^4 - 6x^2 + 2x - 1 ]  =

 

x^4  - 3x^2 + 2   - x^4 + 3x^2 - x + 1   =

 

-x + 3

 

The smallest possible degree ( as found by the guest)  =   1

 

 

cool cool cool

 Aug 1, 2022

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