Question

Solve the following equation by factorisation method:

`5sqrt3x^2 + 7x-2sqrt3 = 0`

Answer 1

Given:

`5sqrt3x^2 + 7x-2sqrt3 = 0`

Multiply the equation by `sqrt3`​

`15x^2+7sqrt3​x−6=0`

a = 15, b = `7sqrt3`​, c = −6

a × c

= 15 × (−6)

= −90

product = −90

sum = `7sqrt3`

`10sqrt3 and -3sqrt3`

`15x^2 + 10sqrt3x - 3sqrt3 x -6 = 0`

`(15x^2+10sqrt3x) - (3sqrt3x + 6) = 0`

`5x(3x + 2sqrt3)-sqrt3(3x+2sqrt3) = 0`

`(3x + 2sqrt3)(5x-sqrt3) = 0`

`3x+2sqrt3 = 0`

`x = -(2sqrt3)/3`

`5x-sqrt3 = 0`

`x = sqrt3/5`

`x = -(2sqrt3)/3` or `x = sqrt3/5`