Question

If alpha and beta are zeroes of a quadratic polynomial x2+5 then form a quadratic polynomial whose zeroes are 1+alpha and 1+beta

Answer 1

Given : α and ß are zeroes of f(x) = x 2 – 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 x 2 – 6x + 11

{NOTE :- AFTER α and ß are zeroes of f(x) = x 2 – 2x + 3 THIS DIAGRAM WILL COME }

Answer 2

GIVEN 

f(x) = x²-2x+3 are α and β  of zeros

α and β = -(-2)/1 = 2
and αβ =3/1 = 3

(α +2) + (β +2) = α+β+4 
                        = 2+4 = 6

(α+2)+(β +2) = αβ +2 (α+β) +4 
                     =3+2 × 2+4 = 11

 the requires polynomial is x²-6x+11