Question

Solve the following equation using quadratic formula:

3x² – 8x + 2 = 0

Answer 1

Comparing equation 3x² – 8x + 2 = 0 with ax² + bx + c = 0, we get:

a = 3, b = –8 and c = 2

By formula,

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

Substituting values we get:

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

= `(8 ± sqrt(64 - 24))/6`

= `(8 ± sqrt(40))/6`

= `(8 ± sqrt(4 xx 10))/6`

= `(8 ± 2sqrt(10))/6`

= `(2(4 ± sqrt(10)))/6`

= `((4 ± sqrt(10)))/3`

= `(4 + sqrt(10))/3` or `(4 - sqrt(10))/3`

Hence, `x = {(4 + sqrt(10))/3, (4 - sqrt(10))/3}`.