Substituting x = 3 into the function: f(3) = 2(3)^2 - 8(3) + 6 = 18 - 24 + 6 = 0.

Substituting x = 2 into the function gives f(2) = 2^2 - 4(2) + 4 = 0.

For a double root, the discriminant must be zero: b^2 - 4ac = 0. Here, 4^2 - 4(1)(k) = 0. Thus, 16 - 4k = 0, leading to k = 4.

Subtract 2 from both sides: 3x > 9. Then divide by 3: x > 3.

Subtract 4 from both sides: 3x > 6. Then divide by 3: x > 2.

The polynomial can be factored as (x + 1)(x + 1) or (x + 1)^2. Thus, the roots are x = -1 and x = -1.

To find the roots, we can factor the polynomial: x^2 + 2x - 8 = (x + 4)(x - 2). Setting each factor to zero gives us x + 4 = 0 or x - 2 = 0, so the roots are x = -4 and x = 2.

To find the roots, we can factor the polynomial: x^2 - 5x + 6 = (x - 2)(x - 3). Setting each factor to zero gives us x - 2 = 0 or x - 3 = 0, so the roots are x = 2 and x = 3.

The sum of the roots of a quadratic ax^2 + bx + c is given by -b/a. Here, b = 6 and a = 1, so the sum is -6/1 = -6.

The inequality x^2 - 4 < 0 can be factored as (x - 2)(x + 2) < 0. The solution set is -2 < x < 2.

The polynomial can be factored as (x + 2)(x + 2) or (x + 2)^2. Therefore, x + 2 is a factor.

To solve the inequality, subtract 2 from both sides: x > 1.

Subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.