AMATHS HELP!! Im a maths idiot =(

1. Given the equation (3+m)x^2 - (8+4m)x + (3+4m) = 0, find the value of m for which
(i) one root is the negative of the other ans: m=(-2)
(ii)one root is the reciprocal of the other ans: m=0

2. Show that the equation 6x^3 - 5x^2 + 10x - 3 = 0 cuts the x axis at only one point

(1)
If r1 and r2 are the roots of ax² + bx +c =0

then
r1+r2 = -b/a
(r1)*(r2) = c/a

in case (i), we have r1 = -r2

r1+r2 = 0 ==> -b/a =0 ==> b = 0

b = 8+4m = 0 ==> 4m= -8 ==> m = -2

in case (ii), we have r1 = 1/r2

r1*r2 = 1 ==> c/a = 1 ==> c=a

3+m = 3+4m ==> m=4m ==> m=0

(2)
6x³ -5x² +10x - 3 = (3x-1)(2x²-x+3)

The only root is x=1/3 because the discriminant for 2x²-x+3=0 is

(-1)² - 4(3)(2) = -23 <0

(3+m)x^2 - (8+4m)x + (3+4m) = 0,
Sum of roots = (8+4m)/(3+m) ............(i)
Product of roots = (3+4m)/(3+m) .........(ii)
let one root is p then other root -p
therefore p-p =0 = (8+4m)/(3+m) = 0
8+4m = 0 or m = -2 .............Ans
(p)(1/p) =1 = (3+4m)/ (3+m)
3+4m = 3+m
3m =0 or m= 0 .........Ans

I'm not completely sure, but I know you can break that down into two equations.
Equation 1: (3+m) - (8+4m) + (3+4m) = 0
Equation 2: x^2 - x + 1 = 0

I'm sorry I can't be of more help. :[

so x1+x2=0
8+4m/3+m=0
8=-4m
m=-2
-----------------------------------
x1x2=1
3+4m/3+m=1
3+4m=3+m
3m=0
m=0
-------------------------------------
God bless you.