if alpha and beta are the zeroes of the quadratic polynomial f(x)=x square-2x+3 then find a quadratic polynomial whoes zeroes are alpha+2 and beta+2

Question

If alpha and beta are the zeroes of the quadratic polynomial f(x)=x

Answer 1

Given : α and ß are zeroes of f(x) = x² – 2x + 3

So,

Now, (α + 2) + (ß + 2) = α + ß + 4 = 2 + 4 = 6

and (α + 2) (ß + 2) = αß + 2 (α + ß) + 4 = 3 + 2 × 2 + 4 = 11

So required polynomial is x² – 6x + 11