Which of the following is a root of the quadratic equation, 3x² + 13x + 14 = 0 ?

1. $-\dfrac{1}{3}$

2. $-\dfrac{3}{2}$

3. $-\dfrac{5}{3}$

4. $-\dfrac{7}{3}$

If x = $\dfrac{-1}{2}$ is a solution of the quadratic equation 3x² + 2kx - 3 = 0, then the value of k is:

1. $-\dfrac{3}{4}$

2. $-\dfrac{5}{4}$

3. $-\dfrac{9}{4}$

4. $-\dfrac{4}{5}$

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:

1. |a| ≥ 2

2. |a| ≤ 2

3. |a| > 2

4. |a| < 2

The positive value of k for which the equations x² + kx + 64 = 0 and x² - 8x + k = 0 will both have real roots, is

1. 16

2. 8

3. 12

4. 4