SOLUTION: For the function f(x)=x^2-2x+1 (a)find f(0) (b)solve f(x)=0

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Question 124256This question is from textbook Structure and Method Book 1
: For the function f(x)=x^2-2x+1
(a)find f(0)
(b)solve f(x)=0
 This question is from textbook Structure and Method Book 1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
f%28x%29=x%5E2-2x%2B1
(a)find f%280%29
f%280%29=0%5E2-2%2A0+%2B1
f%280%29=+1


(b)solve f(x)=0
+x%5E2-2x%2B1+=+0


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-2%2Ax%2B1=0 ( notice a=1, b=-2, and c=1)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=1




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A1+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B-4+%29%29%2F%282%2A1%29 Multiply -4%2A1%2A1 to get -4




x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+0%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+0%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%282+%2B+0%29%2F2 or x+=+%282+-+0%29%2F2


Lets look at the first part:


x=%282+%2B+0%29%2F2


x=2%2F2 Add the terms in the numerator

x=1 Divide


So one answer is

x=1




Now lets look at the second part:


x=%282+-+0%29%2F2


x=2%2F2 Subtract the terms in the numerator

x=1 Divide


So another answer is

x=1


So our solutions are:

x=1 or x=1


which means we only have one solution


x=1