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Question

# Find the factors of 6x2−13x+6=0

A

(x2)(2x3)

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B

(3x1)(2x3)

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C

(3x2)(x3)

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D

(3x2)(2x3)

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Solution

## The correct option is D (3x–2)(2x–3) 6x2−13x+6 ----->(1) Using the method of splitting the middle term. x term is the sum of two factors and product equal to the last term. Here a = 6,b = -13,and C = 6 a.c = Product of 6 and 6 = 36 Factors of 36 = 2,18 = 3,12 = 4,9 Only the factors 4 and 9 gives 13 ⟶ (4 + 9) For -13 , both the factors have negative sign. (- 4 - 9 = - 13) Equation (1) ⇒ 6x2−4x−9x+6 ⇒2x(3x–2)–3(3x–2) ⇒(3x–2)(2x–3) are the factors.

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