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Q.

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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a

–2 and 5

b

–4 and –5

c

–2 and –7 

d

2 and 7 

answer is A.

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Detailed Solution

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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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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.