Question

If alpha and beta are zeros of the polynomial 21x^2-x-2 find a quadratic polynomial whose zeros are 2 alpha and 2 Beta

Answer 1

Answer:

21x^2-42x-84

Step-by-step explanation:

if alpha and beta are two zeroes of polynomial

then,sum of the zeroes (alpha+beta)=(-coefficient of x)/(coefficient of x^2)=-(-1/21)=1/21

if zeroes are 2 alpha and 2 beta then,

sum of the zeroes = 2alpha+2beta=2(alpha+beta) =2(1/21)=2/21

product of the zeroes =( constant term/coefficient of x^2)=(-2/21)

if zeroes are 2alpha and 2beta,then

2alpha × 2beta = 2(alpha×beta)=2(-2/21) = (-4/21)

by the formula,

K[x^2-(alpha+beta)x + (alpha×beta)]

k[x^2 -(2/21)x +(-4/21)]

21[x^2- 2x -4]

= 21x^2 - 42x -84