Question

If alpha and beta r the zeroes of the polynomial x²-x-2 find the polynomial whose zeroes are 2*alpha+1 and 2beta+1

Answer 1

from the polynomial f(x) = x2-x-2 we get, alpha +beta = -b/a

=1 and product of zeroes alpha * beta = (-2)

sum of the zeroes of the other polynomial g(x) say = (2alpha+1)+(2beta+1) = 2(alpha+beta)+2=4

product of its zeroes = (2alpha+1)(2beta+1) = 4 *alpha*beta+2(alpha+beta)+1

= -8+2+1= -5

therefore the other polynomial g(x) = [x2-(sum zeroes)x+product of zeroes] = x2-4x-5