Question

If alpha and beta are the zero of the polynomial x2-x-2 find a polynomial whose zeros are 2alpha+1 and 2beta+1

Answer 1

x2-x-2=0
x2-2x+x-2=0
x(x-2)+1(x-2)=0
(x-2) , (x+1)=0
x=2, x=-1
Let alpha =2 and beta =-1
Zeroes of another polynomial
2alpha+1 and 2beta+1
2(2)+1 and 2(-1)+1
4+1=5
-2+1=-1
Polynomial =x2-(5-1)x+(5)(-1)=0
x2-4x-5=0 is the polynomial.