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Consider the polynomial f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 and g(x) = 3 - 2x - 6x^3 + 19x^4. Find c such that the polynomial f(x) + cg(x) has degree 3.

 Jan 22, 2022
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Consider the polynomial f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 and g(x) = 3 - 2x - 6x^3 + 19x^4. Find c such that the polynomial f(x) + cg(x) has degree 3.

 

\(f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 \)

 

\(g(x) = 3 - 2x - 6x^3 + 19x^4\)

 

Looking just at the x^4 term

   \(f(x) + cg(x)=..... 5x^4+c*19x^4\\ f(x) + cg(x)=..... (5+19c)x^4\)

 

if the x^4 term is to disappear then    5+19c=0     etc

 Jan 22, 2022

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