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Solve the following quadratic equations by factorization.

$3 x + 1 − 12 = 2 3 x − 1, x ≠ − 1, 13$

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1, 5

1, 2

2, 7

1, 3

answer is D.

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Detailed Solution

Given, 3 x + 1 − 12 = 2 3 x − 1, x ≠ − 1, 13

⇒ 3 x + 1 − 2 3 x − 1 = 12 ⇒ 3 (3 x − 1) − 2 (x + 1) (x + 1) (3 x − 1) = 12 ⇒ 9 x − 3 − 2 x − 2 3 x 2 + 3 x − x − 1 = 12 ⇒ 7 x − 5 3 x 2 + 2 x − 1 = 12

Cross multiplying,

⇒ 2 (7 x − 5) = 3 x 2 + 2 x − 1 ⇒ 14 x − 10 = 3 x 2 + 2 x − 1 ⇒ 0 = 14 x − 10 − 3 x 2 − 2 x + 1 ⇒ 3 x 2 − 12 x + 9 = 0

⇒ 3 x (x − 3) − 3 (x − 3) = 0 ⇒ (3 x − 3) (x − 3) = 0

Since,

(3 x − 3) = 0

and

(x − 3) = 0

Values are

x = 1

and

x = 3

Therefore, the values of x which satisfies the given quadratic equation are 1 and 3 and the correct option is 4.

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