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pickupchik [31]
3 years ago
5

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 2b

eta + 1​
Mathematics
1 answer:
frosja888 [35]3 years ago
5 0

Answer:

Step-by-step 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.

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