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

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Solution

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

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