Question

How can you describe the solution set of the equation 16x2 - 8x + 1 = 0?

There are two different real solutions because the expression has two different factors.

There are two different real solutions because the expression has three terms.

There is one real solution because the expression’s factors are the same.

There are no real solutions because the expression cannot be factored.

Answer 1

Answer:

32-8x+1=0

-8x=-33

x=-33/8

Answer 2

Answer :

★Third option : There is one real solution because the expression’s factors are the same.

: is correct

______________________________

★Reason :

Let's take the equation :

16x² - 8x + 1= 0

Now splitting the middle term we have

→16x² -4x -4x +1 = 0

→4x(4x -1)-1(4x - 1) = 0

→(4x -1)(4x-1)= 0

Now solutions are :

4x - 1 =0 and 4x -1=0

→4x = 1 , →4x = 1

→x = 1/4 , →x = 1/4

From above we can conclude that , we found two factors of the questioned expression 16x²-8x+1=0 , then we solve the equation and found two real solutions i.e. x = 1/4 and x = 1/4 . But wait if we observe both the factors (4x +1) and other (4x+1) , both are same . Even the solutions are also same 1/4

Therefore , There is one real solution because the expression’s factors are the same.