Question

If alpha and beta are zeros of quadratic polynomial f (x) = x^2 - x-2 . Find a polynomial whose zeros are 2 alpha + 1 and 2 Beta + 1.

Answer 1

F(x) = x2-x-2
Let alpha be A and beta be B
Now A+B= 1/1=1
And AB= -2
Let the other polynomial be
ax2+bx +c whose zeroes are 2A+1 and 2B+1
Sum of zeroes = 2A+1+2B+1= 2(A+B(+2= 2*1+2=4
And
Product of zeroes = (2A+1)(2B+1)=4AB+2A+2B +1= 4*(-2)+2+1= -5
Now the required polynomial is
=k[x2-(sum of zeroes)x+product of zeroes ]
=k[x2-x-5] [ k is constant ]
When k =1 then
X2-x-5 is the required polynomial