If the quadratic equation 12x2 + 13x – 14 = 0 can be written as (3x + a) (4x – b) = 0, then find the respective values of a and b.

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If the quadratic equation 12x² + 13x – 14 = 0 can be written as (3x + a) (4x – b) = 0, then find the respective values of a and b.

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–2 and 5

–4 and –5

–2 and –7

2 and 7

answer is A.

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Consider the equation 12x² + 13x – 14 = 0.

⇒ 12x² + 21x – 8x – 14 = 0

⇒ 3x(4x + 7) – 2(4x + 7) = 0

⇒ (4x + 7)(3x – 2) = 0

⇒ (3x – 2)(4x + 7) = 0

By comparing this equation with the equation (3x + a) (4x – b) = 0, we obtain a = –2 and b = –7.

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