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If f(x)=x^3-(a+b)x^2 +abx, find the value of f(a). What is the significance of x-a?
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High School Teacher
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Given `f(x)=x^3-(a+b)x^2+abx` :
(a) Determine f(a):
We can factor f(x): first factor out the common x
`f(x)=x(x^2-(a+b)x+ab)` The term in the parantheses factors:
Now it is clear that f(a)=0. **f(a)=a(a-a)(a-b)=a*0*(a-b)=0 **
Alternatively you can substitute a for x:
(b) What is the significance of (x-a)? x-a is a linear factor of f(x); thus a is a root (or zero or solution) of f(x).
Posted by embizze on July 12, 2013 at 1:05 AM (Answer #1)
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