Question

i'm studying for a test and i've just got a few questions..
1-If x^2+8x+m has one double root then m=? and the vertex is?

2-I got -3-i(s.r)5 / 5 for this problem-> -15-(s.r)-125.. is that correct?

3-Is the answer for (5-3i)^2 -30i+ 16 ?

4-is the answer to the formula 25x^2-20x+1 in simplest radical form 2+/-(s.r)3/10?

Answer 1

1. If x^2 + 8x + m has a double root if it is a perfect square. Select a value of m that makes it one

2. Is the problem to rewrite
-15 - sqrt(-125)?
If so, the two different expressions you wrote are not equal

3. 25 -30i -9 = -30i + 16. yes

4. You have written a polynomial expression but not an equation. Expressions can be rearranged but do not have "solutions". If you are looking for the soution to
25x^2 -20x +1 = 0, what you wrote is not it. The first term would be 20/50 = 2/5

Answer 2

1. if there is a double root, then the curve must touch the x-axis, and the factors must be x-a)(x-a), where a is the contact value on the x-axis

which means that x^2 + 8x + m must be a perfect square, looks like m has to be 16

and the x-axis contact point would be (4,0)
So what do you think about the vertex?

2. Are you simplifying -15 - √-125 ?

if so, then
-15 - √-125
= -15 -5√25*√-1
= -15 - 25i

were you trying to factor that? if so, then
= -5(3 + 5i)

3. ????

4. your wording is horrible
are you asking to solve 25x^2-20x+1 = 0 by the quadratic formula?

then x = (20 ± √300)/50
= (20 ± 10√3)/50
= (2 ± √3)/5