x= b±√(b^2 4ac)2a Here a=12,b= 7,c=1 x=7±√(( 7)^2 4× 12× 1)2× 12 x=7±√(49 48)24 x=7± 124 x=824 or x=624 x=13 or x ...

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(a+b)(a-b) Expansion and Visualisation

Factorise: ...

Question

Factorise: $12 x^{2} - 7 x + 1$

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Solution

The given quadratic equation is $12 x^{2} - 7 x + 1$
$= 12 x^{2} - (4 + 3) x + 1$
$= 12 x^{2} - 4 x - 3 x + 1$
$= 4 x (3 x - 1) - 1 (3 x - 1)$
$= (3 x - 1) (4 x - 1)$
$∴ 12 x^{2} - 7 x + 1 = (3 x - 1) (4 x - 1)$

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