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?

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

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

Sure, I'd be happy to help you with your questions! Here are the answers and explanations for each of them:

1. If the quadratic equation x^2 + 8x + m has one double root, it means that the discriminant of the equation is zero. The discriminant of a quadratic equation ax^2 + bx + c is given by b^2 - 4ac. So in this case, we have 8^2 - 4(1)(m) = 0. Simplifying this equation, we get 64 - 4m = 0. Solving for m, we have 4m = 64, and dividing both sides by 4 gives us m = 16. Therefore, m is 16.

To find the vertex of the quadratic equation, we can use the formula x = -b/2a. In this case, a = 1 and b = 8. Plugging in these values, we get x = -8/2(1) = -4. To find the corresponding y-coordinate, we substitute x = -4 into the equation. So y = (-4)^2 + 8(-4) + 16 = 0. Therefore, the vertex is (-4, 0).

2. To simplify the expression (-3 - i(sqrt(5))) / 5, we need to rationalize the denominator. Multiply the numerator and denominator by the conjugate of the denominator, which is 5. So we have:

[(-3 - i(sqrt(5))) / 5] * [5 / 5] = (-3 - i(sqrt(5))) / 25

Expanding the numerator, we get -3/25 - i(sqrt(5))/25. Therefore, the simplified expression is (-3/25) - (i(sqrt(5))/25).

For the second part, to simplify -15 - i(sqrt(-125)), we need to simplify the square root of -125. The square root of -125 can be written as i(sqrt(125)). Simplifying further, we have i * 5(sqrt(5)). Substituting this into the expression, we get: -15 - i * 5(sqrt(5)). The final answer is -15 - i * 5(sqrt(5)).

3. To find the answer for (5 - 3i)^2 - 30i + 16, we can first square the complex number. (5 - 3i)^2 is equal to (5^2 - 2 * 5 * 3i + (3i)^2), which simplifies to (25 - 30i + 9i^2). Since i^2 is equal to -1, we can substitute that value: (25 - 30i + 9(-1)). Simplifying further, we get: (25 - 30i - 9). Combining like terms, this becomes (16 - 30i). Adding -30i + 16, we get the final answer of -30i + 16.

4. The quadratic equation 25x^2 - 20x + 1 is in simpler form and cannot be further simplified by expressing it with radicals. Therefore, the answer to the formula 25x^2 - 20x + 1 in simplest radical form is 25x^2 - 20x + 1 itself.

I hope this helps! Let me know if you have any further questions.