Question

if alpha and beta are zeroes of the quadratic polynomial f(x) = x2-x-2 then find a polynomial whose zeroes are 2alpha + 1 and 2beta + 1​

Answer 1

Explanation:

Hello, as alpha and beta are zeroes of

`x^2-x-2`

it means that their sum is alpha+beta=1 and their product alpha*beta=-2.

The polynomial whose zeroes are 2 alpha + 1 and 2 beta + 1, means that the sum of its zeroes is 2(alpha+beta)+2=2+2=4

and the product is (2alpha+1)(2beta+1)=4 alpha*beta + 2(alpha+beta) + 1 = 4 * (-2) + 2*(1) +1 = -8 + 2 + 1 = -5. so one of these polynomials is

`\Large \boxed{\sf \bf \ \ x^2-4x-5 \ \ }`

Thank you.