Question

find a polynomial whose zeroes are 2,1 and -1 what is its degree.

Answer 1

alpha+beta+gama=-b/a
2+1+-1=-b/a
2=-b/a

alpha*beta*gama=-d/a
2*1*-1=-d/a
-2=-d/a

alpha beta+beta gama+gama alpha=c/a
2*1+1*-1+-1*2=c/a
-1=c/a
a=1, b=-2, c=-1, d=2
polynomial is
x4-2x3-x2+2

Answer 2

Answer:

$x^3-2x^2-x+2=0$

Degree is 3

Step-by-step explanation:

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

To find : The polynomial and its degree

Solution :

Zeros are the roots of the polynomial so,

x=2,1,-1

Roots are (x-2)(x-1)(x+1)

Equate roots to zero and find the polynomial

$(x-2)(x-1)(x+1)=0$

$(x-2)(x^2-1)=0$

$x^3-x-2x^2+2=0$

Required polynomial $x^3-2x^2-x+2=0$

Zeros of the polynomial are 3 so, the polynomial is with the degree 3.