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Solve the following quadratic equations by factorization:

$4 x − 3 = 5 2 x + 3, x ≠ 0, − 32$

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2, -2

1, -2

3, -4

4, -2

answer is B.

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Detailed Solution

Given,

4 x − 3 = 5 2 x + 3, x ≠ 0, − 32

⇒ 4 x − 3 = 5 2 x + 3 ⇒ 4 − 3 x x = 5 2 x + 3

Cross-multiply and solve,

⇒ (4 − 3 x) (2 x + 3) = 5 x ⇒ 8 x − 6 x 2 + 12 − 9 x = 5 x ⇒ 6 x 2 − 8 x − 12 + 9 x + 5 x = 0 ⇒ 6 x 2 + 6 x − 12 = 0

Divide both sides by 6,

⇒ 16 6 x 2 + 6 x − 12 = 16 × 0 ⇒ x 2 + x − 2 = 0

⇒ x 2 + 2 x − x − 2 = 0 ⇒ x (x + 2) − 1 (x + 2) = 0 ⇒ (x − 1) (x + 2) = 0

⇒

x - 1 = 0

x + 2 = 0

⇒

x = 1, - 2

Hence, the correct option is 2.

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