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Consider the polynomials
f(x)=1-12x+3x^2-4x^3+5x^
and
g(x)=3-2x-6x^3+9x^4
Find c such that the polynomial f(x)+cg(x) has degree 3.

 Jul 28, 2020
 #1
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f(x)  =  1 - 12x + 3x2 - 4x3 + 5x4         g(x)  = 3 - 2x - 6x3 + 9x4

 

Find  c  such that the polynomial  f(x) + c·g(x)  has degree 3.

 

To have degree 3 means that the result must have a term or degree 3 and no term with a deree larger than 3.

 

So, we need a value for  c  such that when multiplied by the fourth-degree term of  g(x)  and added to the

fourth-degree term of  f(x)  those fourth-degree terms will cancel.

 

Try  - 5/9   --->

( 1 - 12x + 3x2 - 4x3 + 5x4 )  +  (-5/9) · ( 3 - 2x - 6x3 + 9x4 )

=  1 - 12x + 3x2 - 4x3 + 5x4 - (5/9)(3) - (5/9)(-2x) - (5/9)(-6x3) - (5/9)(9x4)

=   ........

 

(I'll let you finish.)

 Jul 28, 2020

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