Question

Solve the following equation using quadratic formula:

`3/4 x^2 - x - 1 = 0`

Answer 1

Comparing equation `3/4 x^2 - x - 1 = 0` with ax² + bx + c = 0, we get:

a = `3/4`, b = –1 and c = –1

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(-1) ± sqrt((-1)^2 - 4(3/4)(-1)))/(2(3/4))`

= `(1 ± sqrt(1 + 3))/((3/2))`

= `(1 ± sqrt(4))/((3/2))`

= `(1 ± 2)/((3/2))`

= `(2(1 ± 2))/3`

= `(2 ± 4)/3`

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

= `6/3` or `(-2)/3`

= 2 or `(-2)/3`

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