Solve equations, using facrorization method :
$2 x^{2} - 9 x + 10 = 0$ when:
$x \in N$

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Solution

Step : Factorising the equation when $x \in N :$
$2 x^{2} - 9 x + 10 = 0$
$2 x^{2} - 5 x - 4 x + 10 = 0$ {factorizing left hand side}
$\Rightarrow x (2 x - 5) - 2 (2 x - 5) = 0$
$\Rightarrow (2 x - 5) (x - 2) = 0$
$\Rightarrow 2 x - 5 = 0$ or $x - 2 = 0$
{zero product rule}
$\Rightarrow x = \frac{5}{2}$ or $x = 2$ given $x \in N,$
we have $x = 2. {N \to natural number}$
$∴ x = 2$
Hence, the required answer is $x = 2$ .

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