Solve, $12 x^{2} - 7 x + 1 = 0$

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Solution

Consider the given equation.

$12 x^{2} - 7 x + 1 = 0$

$12 x^{2} - 4 x - 3 x + 1 = 0$

$4 x (3 x - 1) - 1 (3 x - 1) = 0$

$(4 x - 1) (3 x - 1) = 0$

$4 x - 1 = 0 \Rightarrow x = \frac{1}{4}$

$3 x - 1 = 0 \Rightarrow x = \frac{1}{3}$

Hence, the values of $x$ are $\frac{1}{3}, \frac{1}{4}$ .

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∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} - 1 & x^{2} + 2 x + 1 & 2 x^{2} + 3 x + 1 2 x^{2} + x - 1 & 2 x^{2} + 5 x - 3 & 4 x^{2} + 4 x - 3 6 x^{2} - x - 2 & 6 x^{2} - 7 x + 2 & 12 x^{2} - 5 x - 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

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

12 x^{2} - 7 x - 1

12 x^{2} - 27 = 0

{12 x}^{2} + 25 x + 12 = 0

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