Find G.C.D of $20 x^{2} - 9 x + 1$ and $5 x^{2} - 6 x + 1$

(x-1)

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(5x-1)

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(5x+1)

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None of these

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Solution

The correct option is C (5x-1)
Let, $p (x) = 20 x^{2} - 9 x + 1$ and $q (x) = 5 x^{2} - 6 x + 1$
$p (x) = 20 x^{2} - 9 x + 1$
$= 20 x^{2} - 5 x - 4 x + 1$
$= 5 x (4 x - 1) - 1 (4 x - 1)$
$= (5 x - 1) (4 x - 1)$
and
$q (x) = 5 x^{2} - 6 x + 1$
$= 5 x^{2} - 5 x - x + 1$
$= 5 x (x - 1) - 1 (x - 1)$
$= (5 x - 1) (x - 1)$
$∴$ G.C.D of $p (x)$ and $q (x) = (5 x - 1)$ .
Option B is correct.

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