The equation has two distinct real roots, if

For what values of b, the quadratic equation 4x² + bx + 16 = 0 has equal real roots?

Determine the nature of the roots of the quadratic equation 3x² + 2x + 5 = 0.

Find the value of K if the quadratic equations $$2x^2 + Kx + 8 = 0 \quad \text{and} \quad 3x^2 + 4x + 12 = 0$$ have both roots common.​

How many real roots does the continuous function f of a variable x shown below have in the interval 0.5 < x < 4.5?