Question

Find the roots of the following quadratic equations by factorisation:

(i) x2 – 3x – 10 = 0​

Answer 1

`\\ \rm\rightarrowtail x^2-3x-10=0`

`\\ \rm\rightarrowtail x^2-5x+2x-10=0`

`\\ \rm\rightarrowtail x(x-5)+2(x-5)=0`

`\\ \rm\rightarrowtail (x+2)(x-5)=0`

`\\ \rm\rightarrowtail x=-2\;or\:5`

Answer 2

Given,

`\small\bold{x² – 3x – 10 =0}`

Taking LHS,

`\small\bold\red{ → }\small\bold{x^2 – 5x + 2x – 10}`

`\small\bold\red{ → }\small\bold{ x(x – 5) + 2(x – 5)}`

`\small\bold\red{ → }\small\bold{ (x – 5)(x + 2)}`

The roots of this equation, x² – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore,
`\small\bold{x – 5 = 0 \: or \: x + 2 = 0}`

`\small\bold\red{ → }\small\bold{x = 5 \: or \: x = -2 }`