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(C) Given equation is $2x^{2} + \frac{5}{3}x - 2 = 0$.On multiplying both sides by $3$,we get:$6x^{2} + 5x - 6 = 0$.To factorise,we split the middle t

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$\frac{-3}{2}, \frac{2}{3}$

Vedclass · Answer

(C) Given equation is $2x^{2} + \frac{5}{3}x - 2 = 0$.On multiplying both sides by $3$,we get:$6x^{2} + 5x - 6 = 0$.To factorise,we split the middle term such that the product of the two numbers is $6 	imes (-6) = -36$ and their sum is $5$. The numbers are $9$ and $-4$.$6x^{2} + 9x - 4x - 6 = 0$Taking common terms:$3x(2x + 3) - 2(2x + 3) = 0$$(2x + 3)(3x - 2) = 0$Now,setting each factor to zero:$2x + 3 = 0 \Rightarrow x = -\frac{3}{2}$$3x - 2 = 0 \Rightarrow x = \frac{2}{3}$Thus,the roots of the equation are $-\frac{3}{2}$ and $\frac{2}{3}$.

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

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