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

x= √15

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x= - √15

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x = √15 or x = - √15

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x = ± 15

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Solution

The correct option is A
x= √15

Given equation is $\frac{2}{5} x^{2} - x - \frac{3}{5} = 0$
On multiplying by 5 on both sides, we get
$\Rightarrow 2 x^{2} - 5 x - 3 = 0 2 x^{2} - (6 x - x) - 3 = 0$ [by splitting the middle term]
$\Rightarrow 2 x^{2} - 6 x + x - 3 = 0 \Rightarrow 2 x (x - 3) + 1 (x - 3) = 0 \Rightarrow (x - 3) (2 x + 1) = 0 N o w, x - 3 = 0 \Rightarrow x = 3 a n d 2 x + 1 = 0 \Rightarrow x = - \frac{1}{2}$
Hence, the roots of the equation $2 x^{2} - 5 x - 3 = 0 a r e - \frac{1}{2} a n d 3$

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