The product of roots of quadratic equation $ax^{2}+bx+C=0,$ is:-

Question

Accepted Answer

The correct option is 3:
To solve this problem, we need to recall Vieta's formulas, which relate the coefficients of a polynomial to the sums and products of its roots.

For a quadratic equation in the standard form $ax^{2}+bx+C=0$, where $a$, $b$, and $c$ are coefficients and $a 
eq 0$, if $\alpha$ and $\beta$ are the roots of the equation, then:  * Sum of the roots: $\alpha + \beta = -\frac{b}{a}$
  * Product of the roots: $\alpha \beta = \frac{c}{a}$The question asks for the product of the roots of the quadratic equation $ax^{2}+bx+C=0$. According to Vieta's formulas, the product of the roots is given by $\frac{c}{a}$.

Therefore, Option 3, which states $\frac{c}{a}$, is the correct answer.

The incorrect option is 1:
Option 1 states $\frac{a}{c}$. This is the reciprocal of the product of the roots and is a common misconception.

The incorrect option is 2:
Option 2 states $\frac{-b}{a}$. This represents the sum of the roots, not the product of the roots. This is another common confusion between the formulas for the sum and product of roots.

The incorrect option is 4:
Option 4 states $\frac{-a}{b}$. This is neither the sum nor the product of the roots and is an incorrect permutation of the coefficients.