Question

if alpha and beta are the zeroes of the quadratic polynomial 21x^2-x-2,find a quadratic polynomial whose zeros are alpha/beta and beta/alpha?

Answer 1

 the polynomial P(x)

we have alpha+beta=-1/21

and,alpha*beta=-2/21

now

P(x)=x2-(sum of zeroes)x+product of zeroes

sop sum of zeroes=

2alpha+2beta=2(alpha + beta)=2*1/21=2/21product of zeroes=

2alpha*2beta=4*alpha*beta

4*(-2/21)= -8/21polynomial= x2-2/21x-8/21

21x2-2x-8=P(x)