Question

If alpha and bita are zeroes of polynomial x^2-2x-15 then find the polynomial whose zeroes are 2alpha and 2bita

Answer 1

hey here is your answer:
since alpha and beta are the zeroes of the polynomial x^2-2x-15
therefore .alpha+beta =-b/a
=-(-2)/1
=2
and alpha*beta=c/a= -15/1= -15
now sum of the zeroes 2alpha and 2beta = 2alpha * 2 beta
=2(alpha+beta)
2*2=4
and product of the series=2alpha *2beta
=4*alpha*beta
=4*(-15)
=(-60)
hence the required polynomial is = k(x^2-(-4)x+(-60))
= k(x^2+4x-60)



hope u understand the answer!!!