Let α, β, γ be the roots of the equation x3+3 a x2+3 b x+c- hat0. If α, β, γ are in H.P. then β is equal to

Question

Let α, β, &gamma; be the roots of the equation x3+3 a x2+3 b x+c- hat0. If α, β, &gamma; are in H.P. then β is equal to (A) - c / b (B) c / b (C) - a (D) a

Tardigrade Admin · Accepted Answer

α+β+&gamma;=-3 a , α β &gamma;=- c α β+β &gamma;+&gamma; α=3 b ⇒ (1/α)+(1/β)+(1/&gamma;)=(3 b /α β &gamma;) ⇒ (2/β)+(1/β)=(3 b /- c ) (∵ α, β, &gamma; text in H.P ) ⇒ (1/β)=-( b / c ) ⇒ β=(- c / b )

Q. Let $α, β, γ$ be the roots of the equation $x^{3} + 3 a x^{2} + 3 b x + c - \hat{0}$ . If $α, β, γ$ are in H.P. then $β$ is equal to

$- c / b$

$c / b$

$- a$

$a$

Q. Let α,β,γ be the roots of the equation x3+3ax2+3bx+c−0^. If α,β,γ are in H.P. then β is equal to

−c/b

c/b

−a

a

α+β+γ=−3a,αβγ=−c αβ+βγ+γα=3b⇒α1​+β1​+γ1​=αβγ3b​ ⇒β2​+β1​=−c3b​(∵α,β,γ in H.P ) ⇒β1​=−cb​⇒β=b−c​

Q. Let $α, β, γ$ be the roots of the equation $x^{3} + 3 a x^{2} + 3 b x + c - \hat{0}$ . If $α, β, γ$ are in H.P. then $β$ is equal to

$- c / b$

$c / b$

$- a$

$a$