Asked by Anonymous
One root of the equation x^2+6x+q=0 is twice the other root. Find q and the roots.
Answers
Answered by
Reiny
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
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
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