The equation 8x3 - ax2 - bx -1 - 0 has three real roots in G-P- If -1 - a -2 - then ordered pair -1- -2 can be

The correct option is C ( 10, 8) Since, a=2b So, a∈ ( ∞, 4] ∪ [12,∞) Hence, ordered pair (λ_1, λ_2) is ( 10, 8). ...

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Mathematics

Roots of a Quadratic Equation

The equation ...

Question

The equation $8 x^{3} - a x^{2} + b x - 1 = 0$ has three real roots in G.P. If $λ_{1} \leq a \leq λ_{2}$ , then ordered pair $(λ_{1}, λ_{2})$ can be

(- 2, 2)

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(18, 12)

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(- 10, - 8)

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none of these

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Solution

The correct option is C $(- 10, - 8)$
Since, $a = 2 b$
So, $a \in (- \infty, 4] \cup [12, \infty)$
Hence, ordered pair $(λ_{1}, λ_{2})$ is $(- 10, - 8) .$

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The equation 8x3−ax2+bx−1=0 has three real roots in G.P. If λ1≤a≤λ2 , then ordered pair (λ1,λ2) can be

The correct option is C (−10,−8)Since, a=2bSo, a∈(−∞,4]∪[12,∞)Hence, ordered pair (λ1,λ2) is (−10,−8).

The equation $8 x^{3} - a x^{2} + b x - 1 = 0$ has three real roots in G.P. If $λ_{1} \leq a \leq λ_{2}$ , then ordered pair $(λ_{1}, λ_{2})$ can be

The correct option is C $(- 10, - 8)$
Since, $a = 2 b$
So, $a \in (- \infty, 4] \cup [12, \infty)$
Hence, ordered pair $(λ_{1}, λ_{2})$ is $(- 10, - 8) .$