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The polynomial f(x) satifies the equation f(x)-f(x-2)=(2x-1)2 for all x. If p and q are the coefficients of x2 and x respectively, in f (x), then what is the value of p+q?

 Oct 16, 2018

Best Answer 

 #1
avatar+27578 
+2

The difference is given by p(x2 - (x-2)2) + q(x - (x-2)) or (4x-4)p + 2q

 

For this to equal (2x - 1)2 we must have 4p = 4 or p= 1 and 2q - 4p = -2, so 2q - 4 = -2 or q = 1

 

p+q = 2

 Oct 16, 2018
 #1
avatar+27578 
+2
Best Answer

The difference is given by p(x2 - (x-2)2) + q(x - (x-2)) or (4x-4)p + 2q

 

For this to equal (2x - 1)2 we must have 4p = 4 or p= 1 and 2q - 4p = -2, so 2q - 4 = -2 or q = 1

 

p+q = 2

Alan Oct 16, 2018

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