Question

Solve the following equation using quadratic formula:

`2x^2 + sqrt(7)x - 7 = 0`

Answer 1

Comparing equation `2x^2 + sqrt(7)x - 7 = 0` with ax² + bx + c = 0, we get:

a = 2, b = `sqrt(7)` and c = –7

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

⇒ `x = (-(sqrt(7)) ± sqrt((sqrt(7))^2 - 4 xx 2 xx (-7)))/(2 xx 2)`

= `(-sqrt(7) ± sqrt(7 + 56))/4`

= `(-sqrt(7) ± sqrt(63))/4`

= `(-sqrt(7) ± sqrt(7 xx 9))/4`

= `(-sqrt(7) ± 3sqrt(7))/4`

= `(-sqrt(7) + 3sqrt(7))/4` or `(-sqrt(7) - 3sqrt(7))/4`

= `(2sqrt(7))/4` or `(-4sqrt(7))/4`

= `sqrt(7)/2` or `-sqrt(7)`

Hence, `x = {-sqrt(7), sqrt(7)/2}`.