One root of the equation x^2+6x+q=0 is twice the other root. Find q and the roots.

Answer 1

Use the properties of roots
for x^2 + bx + c = 0, the sum of the roots is -b and the product of the roots is c
So let the roots be m and 2m
then m + 2m = -6
m = -2
the roots are -2 and -4

m(2m) = q
q = -2(-4) = 8

your equation is x^2 + 6x+ 8 = 0
your roots are -2 and -4

check: if the roots are -2 and -4, we would have
(x+2)(x+4) = 0
x^2 + 6x + 8 = 0 , as needed