What is the solution set for the following quadratic equation?

x2 - 4x + 4 = 0

{-2, 2}

{-2}

{1, 3}

{2}

Question

What is the solution set for the following quadratic equation?

x2 - 4x + 4 = 0
 





{-2, 2}
 




{-2}
 




{1, 3}
 




{2}

anonymous · Answer

2

anonymous · Answer

2

^2 is squared
(+-) is like plus or minus... sorry there's no key for that :)

(-b(+-)√b^2-4AC)/2A

a=1
b=-4
c=4

(4(+-)√4^2-4(1)(4))/2(1)
(4(+-)√16-16)/2
(4(+-)√0)/2
(4(+-)0)/2
since 4 (+-) 0 is always 4, we can cancel that out
4/2
2

whpalmer4 · Answer

$$x^2 - 4x + 4 = 0$$We can factor that if we can think of a pair of factors of 4 that add to -4.  Obviously, both factors must be negative to have a product of +4.  -2 and -2 is such a pair: -2 + -2 = -4, and -2 * -2 = +4.
$$x^2-4x+4 = (x-2)(x-2)$$

$$(x-2)(x-2) = 0$$
For that to be true, at least one of the product terms must = 0:
$$x-2=0$$$$x-2+2 = 0+2$$$$x=2$$

Checking our answer:
$$x^2-4x+4=0$$$$(2)^2-4(2)+4=0$$$$4-8+4=0$$$$0=0\checkmark$$
Therefore the solution set is {2}