You're not done with the first question, you were to show that 2b²=9c

Step 1: Apply Vieta's formulas for the given quadratic equation.
For the quadratic equation $2x^2 + bx + c = 0$, the sum of the roots ($\alpha + \beta$) and the product of the roots ($\alpha \beta$) are given by:

$$\alpha + \beta = -\frac{b}{2} \quad (1)$$ $$\alpha \beta = \frac{c}{2} \quad (2)$$

Step 2: Use the given condition $\alpha = 2\beta$ in the sum of roots equation.
Substitute $\alpha = 2\beta$ into equation (1):

$$2\beta + \beta = -\frac{b}{2}$$ $$$$