Find the factors of 6 x2-13 x-6-0A- 3 x-12 x-3B- 3 x-2x-3C- x-22 x-3D- 3 x-22 x-3

The correct option is D (3x – 2 ) ( 2x – 3) 6x^2 13x + 6 —– gt;(1) Using the method of splitting the middle term. x term is the sum of two factors and pro ...

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Standard VIII

Mathematics

Factorisation by Regrouping Terms

Find the fact...

Question

Find the factors of $6 x^{2} - 13 x + 6 = 0$

(x – 2 ) ( 2x – 3)

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(3x – 1 ) ( 2x – 3)

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(3x – 2 ) ( x – 3)

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(3x – 2 ) ( 2x – 3)

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Solution

The correct option is D
(3x – 2 ) ( 2x – 3)

$6 x^{2} - 13 x + 6$ ----->(1)
Using the method of splitting the middle term.
x term is the sum of two factors and product equal to 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) ⇒ $6 x^{2} - 4 x - 9 x + 6$

⇒2x ( 3x – 2 ) – 3 ( 3x – 2 )

⇒(3x – 2 ) ( 2x – 3) are the factors.

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Find the factors of 6x2−13x+6=0

Find the factors of $6 x^{2} - 13 x + 6 = 0$