If - and - are the roots of the equation x2-kx-9-0 such that - -2- -2- 2 then possible values of -k- is-are where - denotes the greatest integer function

∴ α +β = 5 and αβ =9 nbsp; nbsp; nbsp;α +2β =2αβ ^2 ⇒ k+β =18β⇒β = k17 So, ( k17 )^2+k ( k17 )+9=0 ⇒ k=±514 ...

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Standard XII

Mathematics

Properties of Iota

If α and β ar...

Question

If $α and β$ are the roots of the equation $x^{2} + k x + 9 = 0$ such that $α + 2 β = 2 α β^{2}$ then possible value(s) of [k] is/are (where [•] denotes the greatest integer function)

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Solution

The correct option is C 12
$∴ α + β = - 5 and α β = 9$

$α + 2 β = 2 α β^{2}$

$\Rightarrow - k + β = 18 β \Rightarrow β = - \frac{k}{17}$

So, ${(- \frac{k}{17})}^{2} + k (- \frac{k}{17}) + 9 = 0$

$\Rightarrow k = \pm \frac{51}{4}$

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If α and β are the roots of the equation x2+kx+9=0 such that α+2β=2αβ2 then possible value(s) of [k] is/are (where [•] denotes the greatest integer function)

The correct option is C 12∴ α+β=−5 and αβ=9 α+2β=2αβ2 ⇒−k+β=18β⇒β=−k17 So, (−k17)2+k(−k17)+9=0 ⇒k=±514

If $α and β$ are the roots of the equation $x^{2} + k x + 9 = 0$ such that $α + 2 β = 2 α β^{2}$ then possible value(s) of [k] is/are (where [•] denotes the greatest integer function)

The correct option is C 12
$∴ α + β = - 5 and α β = 9$

$α + 2 β = 2 α β^{2}$

$\Rightarrow - k + β = 18 β \Rightarrow β = - \frac{k}{17}$

So, ${(- \frac{k}{17})}^{2} + k (- \frac{k}{17}) + 9 = 0$

$\Rightarrow k = \pm \frac{51}{4}$