Answer:
q = 8
x₁ = -2, x₂ = -4
Explanation:
For a quadratic equation ax² + bx + c, the sum of the roots is -b/a, and the product of the roots is c/a.
If the roots are x₁ and x₂, then:
-6/1 = x₁ + x₂
q/1 = x₁ x₂
Since we know one root is double the other, we can say x₂ = 2x₁. Plugging into the first equation and solving:
-6 = x₁ + 2x₁
-6 = 3x₁
x₁ = -2
Which means x₂ = -4. So the value of q must be:
q/1 = (-2) (-4)
q = 8