Question

Solve the following equation using quadratic formula:

`sqrt(3)x^2 + 10x - 8sqrt(3) = 0`

Answer 1

Comparing equation `sqrt(3)x^2 + 10x - 8sqrt(3) = 0` with ax² + bx + c = 0, we get:

a = `sqrt(3)`, b = 10 and c = `-8sqrt(3)`

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(10) ± sqrt((10)^2 - 4 xx sqrt(3) xx (-8sqrt(3))))/(2 xx (sqrt(3))`

= `(-10 ± sqrt(100 + 96))/(2sqrt(3))`

= `(-10 ± sqrt(196))/(2sqrt(3))`

= `(-10 ± 14)/(2sqrt(3))`

= `(2(-5 ± 7))/(2sqrt(3))`

= `(-5 ± 7)/sqrt(3)`

= `(-5 + 7)/sqrt(3)` or `(-5 - 7)/sqrt(3)`

= `2/sqrt(3)` or `(-12)/sqrt(3)`

= `2/sqrt(3)` or `(-4 xx 3)/sqrt(3)`

= `2/sqrt(3)` or `-4sqrt(3)`

Hence, `x = {2/sqrt(3), -4sqrt(3)}`.