Question

Find the polynomial whose zeroes are 2, 1 and – 1. What is its degree?

Answer 1

Let the polynomial be p(x).
The factors of p(x) are (x-2)(x-1)(x+1)
(x-2)(x²-1)
x(x²-1)-2(x²-1)
x³-x-2x²+2
x³-2x²-x+2
the degree of the polynomial is 3.

Answer 2

Answer:

The required polynomial is $p(x)=x^3-2x^2-x+2$

The degree of the polynomial is 3.

Step-by-step explanation:

Given : Zeros of polynomial are 2,1 and -1.

To find : The polynomial whose zeros are given ?

Solution :

The polynomial p(x) having zeros 2,1 and -1.

So, factors of the polynomial is (x-2),(x-1),(x+1)

Multiply all the factors to get the polynomial,

$p(x)=(x-2)(x-1)(x+1)$

Apply, $(a-b)(a+b)=a^2-b^2$

$p(x)=(x-2)(x^2-1)$

Multiply,

$p(x)=x^3-x-2x^2+2$

$p(x)=x^3-2x^2-x+2$

The required polynomial is $p(x)=x^3-2x^2-x+2$

The degree of the polynomial is the highest power of the variable i.e. 3.