Question

The sum of the roots of the quadratic equation $a{x}^2+bx+c=0,a\ne 0$ is , while the product of the roots of the quadratic equation is .

• A. $\frac{b}{a}$
• B. $\frac{-c}{a}$
• C. $\frac{c}{a}$
• D. $\frac{-b}{a}$

Answer 1

Answer: (C), (D)

$\frac{-b}{a}$

Given: $a{x}^2+bx+c=0,a\ne 0$
Let $\alpha ,\beta$ be the roots of the given quadratic equation.

Using the relation between roots and coefficients of a qadratic equation,
$\Rightarrow \alpha +\beta =\frac{-\text{Coefficient of}x}{\text{Coefficient of}{x}^2}=-\frac{b}{a}$

$\&\alpha \beta =\frac{\text{Constant term}}{\text{Coefficient of}{x}^2}=\frac{c}{a}$