Question

Use the relationship between zeroes and coefficients of a polynomial and find the sum and product of the polynomial: $4x^3+2x^2-4x-2$.

Answer 1

In the given polynomial,$4x^3+2x^2-4x-2$
$a=4,b=2,c=-4,d=-2$
Relationship between zeroes and coefficient of the polynomial:
Sum of the zeroes $=$ $\frac{Coefficientof{x}^2}{Coefficientof{x}^3}=\frac{-b}{a}$ $=$ $\frac{-2}{4}=\frac{-1}{2}$
Sum of the product of zeroes taken two at a time $=$ $\frac{Coefficientofx}{Coefficientof{x}^3}=\frac{c}{a}$ $=$ $\frac{-4}{4}=-1$
Product of the zeroes $=$ $\frac{-Constantterm}{Coefficientof{x}^3}=\frac{-d}{a}$ $=$ $\frac{-(-2)}{4}=\frac{1}{2}$