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Dividing a Polynomial by a Polynomial

If 5x2-13xy...

Question

If $5 x^{2} - 13 x y + 6 y^{2} = 0$ then $x : y$ is

(2 : 1)

only

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(3 : 5)

only

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(5 : 3)

(1 : 2)

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(3 : 5)

(2 : 1)

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Solution

The correct option is C $(3 : 5)$ or $(2 : 1)$
$5 x^{2} - 13 x y + 6 y^{2}$
$= 5 x^{2} - 10 x y - 3 x y + 6 y^{2}$
$= 5 x (x - 2 y) - 3 y (x - 2 y)$
$= (5 x - 3 y) (x - 2 y)$
$x : y = 3 : 5$
$= 2 : 1$

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