Find the roots of the equation: : $25 a^{2} - 35 a + 12$ .

(5 a - 3) (5 a - 4)

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(5 a - 3) (5 a + 4)

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(5 a + 3) (5 a - 4)

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(5 a + 3) (5 a + 4)

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Solution

The correct option is C $(5 a - 3) (5 a - 4)$
$25 a^{2} - 5 a + 12 = 0$
$⟹ 25 a^{2} - 20 a - 15 a + 12 = 0$
$⟹ 5 a (5 a - 4) - 3 (5 a - 4) = 0$
$⟹ (5 a - 4) (5 a - 3) = 0$
$∴ a = \frac{3}{5}, \frac{4}{5}$

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