### Theory:

Relation between zeroes and the coefficients of a linear polynomial:
If $$\alpha$$ is the zero of the linear polynomial $$p(x) = ax + b$$, then $$\alpha = \frac{-b}{a}$$.

This implies $$\alpha$$ $$=$$ $$\frac{-\left(\text{Constant term}\right)}{\text{Coefficient of }x}$$.
Relation between zeroes and the coefficients of a quadratic polynomial:
If $$\alpha$$ and $$\beta$$ are the zeroes of the quadratic polynomial $$p(x) = ax^2 + bx + c$$, then.

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

This implies sum of the zeroes $$=$$ $$\frac{-\left(\text{Coefficient of }x\right)}{\text{Coefficient of }x^2}$$.

(ii) $$\alpha \beta$$ $$=$$ $$\frac{c}{a}$$

This implies product of the zeroes $$=$$ $$\frac{\text{Constant term}}{\text{Coefficient of }x^2}$$.
Important!
The general form of the quadratic polynomial based on its zeroes is given by:
$$p(x)$$ $$=$$ $$x^2 - \left(\text{Sum of the zeroes}\right)x + \left(\text{Product of the zeroes}\right)$$
Relation between zeroes and the coefficients of a cubic polynomial:
If $$\alpha$$, $$\beta$$ and $$\gamma$$ are the zeroes of the cubic polynomial $$p(x) = ax^3 + bx^2 + cx + d$$, then:

(i) $$\alpha + \beta + \gamma$$ $$=$$ $$\frac{-b}{a}$$

This implies, $$\alpha + \beta + \gamma$$ $$=$$ $$\frac{-\left(\text{Coefficient of }x^2\right)}{\text{Coefficient of }x^3}$$.

(ii) $$\alpha \beta + \beta \gamma + \gamma \alpha$$ $$=$$ $$\frac{c}{a}$$

This implies, $$\alpha \beta + \beta \gamma + \gamma \alpha$$ $$=$$ $$\frac{\text{Coefficient of }x}{\text{Coefficient of }x^3}$$.

(iii) $$\alpha \beta \gamma$$ $$=$$ $$\frac{-d}{a}$$

This implies, $$\alpha \beta \gamma$$ $$=$$ $$\frac{-\left(\text{Constant term}\right)}{\text{Coefficient of }x^3}$$.