Question

Solve the following equation by factorisation method:

`sqrt3x^2 + 10x + 7sqrt3 = 0`

Answer 1

Given:

`sqrt3x^2 + 10x + 7sqrt3 = 0`

Multiply by `sqrt3`​ to remove the surd from the coefficient of x²

`3x2 + 10sqrt3​x + 21 = 0`

product

= 3 × 21 

= 63

sum = `10sqrt3​`

These numbers are:

`7sqrt3​ and 3sqrt3​`

`3x^2+7sqrt3​x+3sqrt3​x+21=0`

`(3x^2+3^3​x)+(7sqrt3​x+21)=0`

`3x(x + sqrt3​) + 7sqrt3​(x + sqrt3​) = 0`

`(x+sqrt3) (3x+7sqrt3)=0`

`x+sqrt3​=0`

⇒ x = `−sqrt3`​

`3x+7sqrt3​=0`

⇒ x = `- (7sqrt3)/3`

x = `−sqrt3`​ or x = `- (7sqrt3)/3`