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Find real numbers a, b, c such that 2x^2 - 8x + 2012 = a + b(x - 2) + c(x - 2)^2.

 May 12, 2020

Best Answer 

 #1
avatar+23552 
+2

Expand to:

a + bx-2b+cx^2-4cx+4c       the only coefficient of x^2 is c    so c = 2

a + bx - 2b + 2x^2-8x+8      the 'x' coefficients have to add to -8  so b =0

a + 2x^2-8x+8                     the constants have to add to 2012     so a = 2004

 

2x^2-8x+2012

 May 12, 2020
 #1
avatar+23552 
+2
Best Answer

Expand to:

a + bx-2b+cx^2-4cx+4c       the only coefficient of x^2 is c    so c = 2

a + bx - 2b + 2x^2-8x+8      the 'x' coefficients have to add to -8  so b =0

a + 2x^2-8x+8                     the constants have to add to 2012     so a = 2004

 

2x^2-8x+2012

ElectricPavlov May 12, 2020

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