Question

if alpha and beta are the zeros of quadratic polynomial
$f(x) = {x}^{2} - x - 2 = 0$
find a polynomial whose zeros are
$2 \alpha + 1 \: and \: 2 \beta + 1$
​

Answer 1

first ,

factorise , x^2 - x - 2

we get (x+1)(x-2)

then , x+1 = 0

x = -1 , alpha

then , x-2 = 0

x = 2 , betta

sum of the zeroes = -b/ a = -(-1)/1 =1

also, alpha + betta = -1 +2 = 1

product of the zeroes = c/ a = -2/1= -2

also , alpha × betta = -1×2 = -2

hence, sum = 1 , product = -2

i hpoe this could be help you....