Using the quadratic formula, x = [4 ± √(16 - 8)] / 4 = [4 ± 2√2] / 4 = 1 ± √2/2. Hence, the roots are not simple fractions.

Using the quadratic formula, the roots are x = [20 ± √(400 - 300)] / 10 = [20 ± 10] / 10 = 3 and 1.

The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.

The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.

The sum of the roots is given by -b/a = 12/3 = 4.

Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.

The sum of the roots is given by -b/a = 7/1 = 7.

The vertex form gives the maximum value at x = 2, f(2) = 5.

The vertex form gives the maximum value at x = 3, f(3) = -3^2 + 6*3 - 8 = 4.

The product of the roots is c/a = -5/2.

Using Vieta's formulas, the product of the roots is 1/2 (c/a = 1/2).

The product of the roots is given by c/a = 2/3.

The product of the roots is given by c/a = 9/3 = 3.

The sum of the roots is given by -b/a = 3/2.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

The vertex can be found using x = -b/(2a) = 4. Substituting x = 4 into the equation gives y = -3.

The discriminant for x^2 + 4x + 5 is negative (16 - 20 < 0), indicating no real roots.