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If , be a real numbers such that x^{3}- x^{2}+ x-6=0 has it

Question

If $λ, μ$ be a real numbers such that $x^{3} - λ x^{2} + μx - 6 = 0$ has its roots real and positive then the minimum value of $μ$ is

3 \times^{3} 36

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0

none of these

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λ, μ

be a real numbers such that

x^{3} - λ x^{2} + μx - 6 = 0

has its roots real and positive then the minimum value of

μ

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Let

α, β, γ

are the roots of

x^{3} - λ x^{2} + μx - 6 = 0

given that roots are real and positive.

α + β + γ = λ

α β + β γ + γ α = μ

α β γ = 6

using the result

A . M \geq G . M

\frac{α β + β γ + γ α}{3} \geq (α^{2} β^{2} γ^{2})^{\frac{1}{3}}

\Rightarrow \frac{μ}{3} \geq (36)^{\frac{1}{3}}

\Rightarrow μ \geq 3 \times (36)^{\frac{1}{3}}

∴

The minimum value of

μ

3 \times (36)^{\frac{1}{3}}

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Question Text	If $λ, μ$ be a real numbers such that $x^{3} - λ x^{2} + μx - 6 = 0$ has its roots real and positive then the minimum value of $μ$ is
Answer Type	Text solution:1
Upvotes	150