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

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

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) (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 we can see that , , and

Start with the discriminant formula

Plug in , , and

Square to get

Multiply to get

Subtract from to get

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

From we can see that , , and

Start with the discriminant formula

Plug in , , and

Square to get

Multiply to get

Subtract from to get

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 we can see that , , and

Start with the discriminant formula

Plug in , , and

Square to get

Multiply to get

Subtract from to get

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

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