Find the roots of the following quadratic equation by factorisation:
$x^{2} - 3 x - 10 = 0$

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Solution

Given equation is $x^{2} - 3 x - 10 = 0$
Here, the middle term $- 3 x$ expressed as sum of $- 5 x$ and $2 x$ such that $- 5 x + 2 x = - 3 x$ and also $- 5 x \times (2 x) = - 10 x^{2} =$ Product of first and last terms of given quadratic equation.
Thus, the given quadratic equation can be written as
$\Rightarrow x^{2} - 5 x + 2 x - 10 = 0$
$\Rightarrow x (x - 5) + 2 (x - 5) = 0$
$\Rightarrow (x - 5) (x + 2) = 0$
$\Rightarrow (x - 5) = 0, (x + 2) = 0$
Therefore, $x = 5, x = - 2$ are the roots of the given quadratic equation.

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