Find the roots of the following quadratic equations by the factorisation method.
$2 x^{2} + \frac{5}{3} x - 2 = 0$

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Solution

Given equation is $2 x^{2} + \frac{5}{3} x - 2 = 0$
On multiplying by 3 on both sides, we get
$6 x^{2} + 5 x - 6 = 0 \Rightarrow 6 x^{2} + (9 x - 4 x) - 6 = 0$ [by splitting the middle term]
$\Rightarrow 6 x^{2} + 9 x - 4 x - 6 = 0 \Rightarrow 3 x (2 x + 3) - 2 (2 x + 3) = 0 \Rightarrow (2 x + 3) (3 x - 2) = 0 N o w, 2 x + 3 = 0 \Rightarrow x = - \frac{3}{2} a n d 3 x - 2 = 0 \Rightarrow x = \frac{2}{3}$
Hence, the roots of the equation $6 x^{2} + 5 x - 6 = 0 a r e \frac{- 3}{2} a n d \frac{2}{3}$

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