Question

If alpha and beta are the zeroes of the polynomial 21y2-y-2 then find a quadratic polynomial,whose zeroes are 2alpha and 2beta

Answer 1

sum of the roots=. -b/a=2(alpha+beta)
product of roots=c/a=4alpha×beta
sum of roots for given is( alpha+beta)=1/21
product of roots is (alpha×beta)=-2/21
2(alpha+beta)=2/21= -(-2/21)
4alpha×beta=-8/21
quadratic polynomial is 21y^2-2y-8

Answer 2

→ Answer :

1/21 (21 x² - 2x + 8)

Since we know that,

→ Sum of zeros = - Coefficient of y/Coefficient of y²

⇒ α + β = - (- 1)/21

⇒ α + β = 1/21

→ Product of zeros = Constant term/Coefficient of y²

⇒ αβ = 2/21

→ S' pf zeros = 2α + 2β

⇒ 2(α + β) = 2 × 1/21

⇒ 2/21

→ P' of zeros = 2α × 2β

⇒ 4αβ = 4 × 2/21

⇒ 8/21

Since we know that,

→ p(x) = k[x² - (Sum of zeros)x + Product of zeros]

Assuming k to be equal to 1, then :

→ p(x) = x² - 2x/21 + 8/21

→ p(x) = (21 x² - 2x + 8)/21

→ p(x) = 1/21 (21 x² - 2x + 8)