Question

if alpha and beta are the zeros of polynomial 3x^2+2x+1find the polynomial whose zeros 1-alpha /1alpha and 1-beta /1+beta​

Answer 1

Step-by-step explanation:

alpha + beta = -b/a = -2/3  -(1)

alpha * beta = c/a = 1/3     -(2)

g(x) = k($x^{2}$ - (sum of zeroes)x +(product of zeroes))

=k($x^{2}$ - (1-alpha/1+alpha + 1-beta/1+beta) +

( 1-alpha/1+alpha*1-beta/1+beta)

by lcam and property of (x-a)(x-b)=x2 - x(a+b) +ab),

=k($x^{2}$- (1 + 2/3 + 1/3)/ (1 + 2/3 +1/3) + (1 + 2/3 + 1/3)/ (1 + 2/3 +1/3))

=k($x^{2}$ -1 +1)

=k($x^{2}$)