Quadratic Polynomial Sum of Zeroes Calculation

The given quadratic polynomial is $ P(x) = 3x^2 + 5x - 2 $.

A general quadratic polynomial is represented as $ ax^2 + bx + c $.

By comparing the given polynomial with the general form, we identify the coefficients:

• $ a = 3 $
• $ b = 5 $
• $ c = -2 $

The formula for the sum of the zeroes $(\alpha + \beta)$ of a quadratic polynomial is given by:

$ \alpha + \beta = -\frac{b}{a} $

Now, substitute the values of $ a $ and $ b $ into the formula:

$ \text{Sum of Zeroes} = -\frac{5}{3} $

Therefore, the sum of the zeroes for the quadratic polynomial $ 3x^2 + 5x - 2 $ is $ -\frac{5}{3} $. This corresponds to Option 4.