SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. 1. 2x2 - 10x + 25 = 0 2. 2x2 - 6x + 5 = 0 3. s2 - 4s + 4 = 0

Algebra ->  Exponents -> SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. 1. 2x2 - 10x + 25 = 0 2. 2x2 - 6x + 5 = 0 3. s2 - 4s + 4 = 0       Log On


   

Question 149469: Determine whether the following equations have a solution or not? Justify your answer.
1. 2x2 - 10x + 25 = 0
2. 2x2 - 6x + 5 = 0
3. s2 - 4s + 4 = 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
They all have a solution. Do you mean if they have a real solution?

To find out if they have real solutions or not, you can use the discriminant formula.

1)


From 2x%5E2-10x%2B25 we can see that a=2, b=-10, and c=25


D=b%5E2-4ac Start with the discriminant formula


D=%28-10%29%5E2-4%282%29%2825%29 Plug in a=2, b=-10, and c=25


D=100-4%282%29%2825%29 Square -10 to get 100


D=100-200 Multiply 4%282%29%2825%29 to get %288%29%2825%29=200


D=-100 Subtract 200 from 100 to get -100


Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.







From 2x%5E2-6x%2B5 we can see that a=2, b=-6, and c=5


D=b%5E2-4ac Start with the discriminant formula


D=%28-6%29%5E2-4%282%29%285%29 Plug in a=2, b=-6, and c=5


D=36-4%282%29%285%29 Square -6 to get 36


D=36-40 Multiply 4%282%29%285%29 to get %288%29%285%29=40


D=-4 Subtract 40 from 36 to get -4


Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.




3)


From s%5E2-4s%2B4 we can see that a=1, b=-4, and c=4


D=b%5E2-4ac Start with the discriminant formula


D=%28-4%29%5E2-4%281%29%284%29 Plug in a=1, b=-4, and c=4


D=16-4%281%29%284%29 Square -4 to get 16


D=16-16 Multiply 4%281%29%284%29 to get %284%29%284%29=16


D=0 Subtract 16 from 16 to get 0


Since the discriminant is equal to zero, this means that there is one real solution