Question

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

Answer 1

Answer:

q = 8

x₁ = -2, x₂ = -4

Step-by-step 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