Question

find the zeroes of the following
without plotting in a graph

1) 2x+1
2) y²-1
3) z³​

Answer 1

Solution (1)

First question is finding the zeroes of the polynomial 2x+1

2x+1 is a linear polynomial. A linear polynomial has only a zero.To find the zeroes,Take 2x+1 =0

2x=-1

x= -1/2

Solution (2)

Second question is finding the zeroes of the polynomial y²-1. This is a quadratic polynomial.

It has two zeroes.To find the zeroes of the polynomial , take y²-1=0

(y+1)(y-1)=0

y= -1 or y= 1

Solution (3)

Third question is finding the zeroes of the polynomial z³. This is a cubic polynomial and it has three zeroes. Take z³=0

z=0

So , zero of the polynomial is 0

NOTE :

A simple trick to find the zeroes of any given polynomial(whether it is linear , quadratic , cubic etc..) is making the value equal to zero and factorising it further.