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f(x) = ax^3+bx^2-4x-3, where a and b are constants.It is given that (x-1) is a factor...

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roshan-rox | Valedictorian

Posted May 25, 2013 at 8:45 PM via web

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f(x) = ax^3+bx^2-4x-3, where a and b are constants.It is given that (x-1) is a factor of f(x).show that a+b = 7

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted May 25, 2013 at 8:57 PM (Answer #1)

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`f(x) = ax^3+bx^2-4x-3`

Since (x-1) is a factor we can say f(1) = 0

`f(1) = 0`

`f(1) = a(1)^3+b(1)^2-4xx1-3`

`0 = a+b-7`

`a+b = 7`

 

So the requirement is shown.

a+b = 7

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abhi4307 | Student , Grade 11 | Valedictorian

Posted May 26, 2013 at 6:04 AM (Answer #2)

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f(x)=ax^3+bx^2-4x-3

q(x)=x-1

Remainder= f(1)=0

a*(1)^3+b*(1)^2-4*1-3=0

a+b=4+3

a+b=7.                    Proved

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