SOLUTION: can you please help me: (((solve f(0)=0 from the function f(x)=x^2-2x+1)))

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: can you please help me: (((solve f(0)=0 from the function f(x)=x^2-2x+1)))      Log On


   

Question 153011This question is from textbook Algebra structure and method book 1
: can you please help me: (((solve f(0)=0 from the function f(x)=x^2-2x+1))) This question is from textbook Algebra structure and method book 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E2-2x%2B1 Start with the given function


0=x%5E2-2x%2B1 Plug in f%28x%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-2, and c=1


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-2, and c=1


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%281%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 4 from 4 to get 0


x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


x+=+%282+%2B+0%29%2F%282%29 or x+=+%282+-+0%29%2F%282%29 Break up the expression.


x+=+%282%29%2F%282%29 or x+=++%282%29%2F%282%29 Combine like terms.


x+=+1 or x+=+1 Simplify.


So the only solution is x+=+1