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Solving a Quadratic Equation by Factorization Method

If 2ax + 1 ...

Question

If $(2 a x + 1) (3 x + 1) = 6 a (x + 1)$ and $x = 1$ , find the value of $a$ .

A

1

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B

4

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C

3

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D

2

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Solution

The correct option is A $1$
$(2 a x + 1) (3 x + 1) = 6 a (x + 1)$
$⟹ [2 a (1) + 1] [3 (1) + 1] = 6 a [(1 + 1)]$
$⟹ (2 a + 1) (3 + 1) = 6 a (2)$
$⟹ (2 a + 1) (4) = 12 a$
$⟹ 8 a + 4 = 12 a$
$⟹ 8 a - 12 a = - 4$
$⟹ - 4 a = - 4$
$⟹ a = 1$

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