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# Math problem

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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

#1
+26399
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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
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#1
+26399
+1

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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