Question

Which of the following is the correct formula for the sum and products of the zeroes of a quadratic polynomial$p\left(x\right)=a{x}^2+bx+c=0$.

• A. $\frac{-b}{a},\frac{c}{a}$
• B. $\frac{-b}{c},\frac{a}{c}$
• C. $\frac{a}{b},\frac{-c}{b}$
• D. none of these

Answer 1

The correct option is A

$\frac{-b}{a},\frac{c}{a}$

Establish relationship between zeroes and coefficient of polynomial.

Sum of the zeroes of a quadratic polynomial$p\left(x\right)=a{x}^2+bx+c=0$ is $\frac{-\mathrm{coefficient}\mathrm{of}x}{\mathrm{coefficient}\mathrm{of}\mathit{}{x}^{\mathit{2}}}=\frac{-b}{a}$

Product of a quadratic polynomial$p\left(x\right)=a{x}^2+bx+c=0$ is $\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}\mathit{}{x}^{\mathit{2}}}=\frac{c}{a}$.

Hence, the correct option is $\mathrm{A}$.