Given α and β are the roots of the quadratic equation x^2-4x+k=0 k≠0. If αβ, αβ^2+α^2β and α^3+β^3 are in geometric progression, then the value of k…

Question

Given α and β are the roots of the quadratic equation x^2-4x+k=0 k≠0. If αβ, αβ^2+α^2β and α^3+β^3 are in geometric progression, then the value of k is equal to

MARKS Content Team · Accepted Answer

Correct answer: (B) 16/7. Here, α+β=4,αβ=k αβ,αβ(α+β) and α+β^3-3αβα+β are in G.P. ⇒4k^2=k64-12k ⇒16k^2=4k16-3k ⇒4k=16-3k ⇒7k=16 ⇒k=16/7

Given $α$ and $β$ are the roots of the quadratic equation $x^{2} - 4 x + k = 0$ $(k \neq 0) .$ If $α β, α β^{2} + α^{2} β$ and $α^{3} + β^{3}$ are in geometric progression, then the value of $k$ is equal to

Solution

More Sequences and Series Questions

Given α and β are the roots of the quadratic equation x2-4x+k=0 k≠0. If αβ, αβ2+α2β and α3+β3 are in geometric progression, then the value of k is equal to

Solution

More Sequences and Series Questions

Given $α$ and $β$ are the roots of the quadratic equation $x^{2} - 4 x + k = 0$ $(k \neq 0) .$ If $α β, α β^{2} + α^{2} β$ and $α^{3} + β^{3}$ are in geometric progression, then the value of $k$ is equal to