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

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

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

594 square inches

step-by-step explanation:

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