Question

if alpha and beta are zeros of x square minus x + 2 find the polynomial whose zeros are 2 alpha + 1 and 2 Beta -1​

Answer 1

I'm writing alpha as @ and beta as ß. So don't get confused.

P(x)=x²-x+2

Sum of zeros=@+ß=-b/a=-(-1)/1

=1

Product of zeros=@ß=c/a=2

Now, for another polynomial,

Sum of zeros= @+1+ß-1

=@+ß

=1

Product of zeros= (@+1)*(ß-1)

=@ß-@+ß-1

=2-1-1

=2

F/K=[x²-(sum of zeros)x+ (product of zeros)]

F/K=x²-x+2