12 x ^ 2 7x 1=0 ∵ x = b±√( b ^ 2 4ac ) #160; 2a = ( 7)±√( ( 7) ^ 2 4.12.( 1) ) #160; 2.12 = 7±√( 97 ) #160 ...

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Factorisation Using Algebraic Identities

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Question

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

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Solution

$12 x^{2} - 7 x - 1 = 0 ∵ x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- (- 7) \pm \sqrt{{(- 7)}^{2} - 4.12. (- 1)}}{2.12} = \frac{7 \pm \sqrt{97}}{24} ∴ x = \frac{7 + \sqrt{97}}{24} o r x = \frac{7 - \sqrt{97}}{24}$

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