List the solutions to the quadratic function below. ALGEBRA 1

Question

f(x)=x^2-4x+5 

 

** Separate your solution values with a comma. For example, x=2,3  or x= 6+√32,6-√32 ** Use MathQuill if you need to **

Answer 1

f(x) = x² - 4x + 5

This is y = x² - 4x + 5

We need to factor and find where y will equal 0.

How do we factor?

Lets look at our x²

^{We will need x & x}

Next look at 5, it will be

1, 5 or 5, 1

Since 5 is positive both factors would need to be the same sign and our middle term is negative.

However when adding -x & -5x it would give us -6x

Either the problem was written incorrectly because if 5 was negative, we could utilize -5x + x to give us -4x.

However, if the problem was written correctly the next step would be complete the square and solve.

We want to know when y will equal 0.

0 = x² - 4x + 5

0 - 5 = x² - 4x + 5 - 5

-5 = x² - 4x Move the 5 to the left side

-5 = x² - 4x

-5 + 4 = x² - 4x + 4

Half the middle term (x term) and square it

-1 = (x - 2)(x - 2)

-1 = (x - 2)²

Now to solve

√-1 = √(× - 2)²

±i = x - 2

Square root of -1 is "i", an imaginary number.

±i + 2 = x - 2 + 2

x = 2 ±i

Check your work:

For 2 + i

y = (2 + i)² - 4(2 + i)+ 5

= 4 + 4i -1 - 8 - 4i + 5

= 9 - 9 = 0

For 2 - i

y = (2 - i)² - 4(2 - i)+ 5

= 4 - 4i -1 -8 + 4i + 5

= 9 - 9 = 0