Can someone help me understand this problem?

Question

I'm taking a class in college, and I've found I've just forgotten so much in the time span since I first took college algebra. Here is what I'm talking about, and it is from properties of the roots section. Can someone show me how this is done?

Find the value of m in the equation 4x^2 + 4x + m = 0 so that one root exceeds the other by 4?

Answer 1

Let 1 root = a

Let the other = a+4

x=[-4 +/- sqrt(16-16 m)]/8 THEN

a = [-4 -sqrt(16-16m)]/8  = [-1-sqrt(1-m)]/2

a+4 = [-4+sqrt(16-16m)]/8=[-1+sqrt(1-m)]/2

Let sqrt(1-m)=p  THEN

2a= -1 - p

2a+8 = -1 + p

subtract 1st eqtn from second, and

2p=8 and p=4

Then m=-15

Answer 2

are you sure of the signs?  without using the quadratic formula, the only thing that really fits is m=1.  factored, that would be

(2x+1)(2x+1) = 4x^2 + 4x +1, but the roots would be the same.

Answer 3

This is a quadratic equation of the form ax^2 + bx + c = 0

4x^2 + 4x + m = 0

In looking at this problem be sure to note that:

a = 4

b = 4

c = m

Sum of the roots = -b/a = -4/4 = -1

Product of the roots = c/a = m/4

Now let one root be r. The other root will then be r + 4.

We know that the sum of the roots = -1.

So:

r + (r + 4) = -1

2r + 4 = -1

r = -5/2

r + 4 = -5/2 + 4 = -5/2 + 8/2 = 3/2

(-5/2)*(3/2) = m/4

m = -15

Answer 4

i dont have an answer to your question, but i wanted to comment on it anyway. I used to love math. I enjoyed it up until they started putting letters in the equations and geometry. i know its a college requirement but in life you will find that you really only need to be able to add and subtract properly and you will be fine.