If α≠β, α2=5α−6,β2=5β−6 then the equation with roots 1α and 1β is

If $α \neq β$ , $α^{2} = 5 α - 6, β^{2} = 5 β - 6$ then the equation with roots $\frac{1}{α}$ and $\frac{1}{β}$ is

A
$6 x^{2} - 5 x + 1 = 0$
B
$6 x^{2} + 5 x + 1 = 0$
C
$6 x^{2} = 5 x - 1 = 0$
D
$6 x^{2} - 5 x - 1 = 0$

Solution:

$α, β$ are the roots of $x^{2} = 5 x - 6$

$\Rightarrow x^{2} - 5 x + 6 = 0$

$\frac{1}{α}$ and $\frac{1}{β}$ are the roots of the equation is

$x^{2} - (\frac{1}{α} + \frac{1}{β}) x + \frac{1}{α} . \frac{1}{β} = 0$

$x^{2} - (\frac{α + β}{α β}) x + \frac{1}{α β} = 0$

$x^{2} - (\frac{5}{6}) x + \frac{1}{6} = 0$

$6 x^{2} - 5 x + 1 = 0$

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