Question

Q.8. Find the roots of the following quadratic equations by factorisation:
x2 – 3x - 10 = 0
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Answer 1

$x^{2} - 3x - 10 = 0$

$x^{2} + 2x - 5x - 10$

$x(x + 2) - 5(x + 2)$

$(x + 2)(x - 5)$

$x = - 2 \: \: \: \: \: or \: \: \: \: x = 5$

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Answer 2

AnswEr

We'll factorize this given equation with the Splitting the middle term method.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies \sf \: {x}^{2} - 3x - 10 =0$

$:\implies \sf \: x(x + 2) - 5(x + 2) =0$

$:\implies \sf \: (x - 5)(x + 2) =0$

$:\implies \sf \:{ \boxed{ \textbf{ \textsf{x = 5 }}}}\: or \: {\boxed{ \textbf{ \textsf{x = - 2}}}}$

In the above example,

We've used the splitting the middle term method, & henceforth,

• Sum = -3

• Product = -10 × 1 = -10

These are used as the factors.

$\therefore$ The 2 roots of the equation are 5 & -2.