Question

Solve the following quadratic equation using formula method only 

 3a²x² +8abx + 4b² = 0, a ≠ 0 

Answer 1

 3a²x² +8abx + 4b² = 0

`"x"^2 + (8"b")/(3"a") "x" + (4"b"^2)/(3"a"^2) = 0`

a = 1 ; b = `(8"b")/(3"a")` ; c = `(4"b"^2)/(3"a"^2)`

D = b² - 4ac

= `((8"b")/(3"a"))^2 - 4(1)((4"b"^2)/(3"a"^2))`

= `(64 "b"^2)/(9"a"^2) - (16 "b"^2)/(3"a"^2)`

= `(64"b"^2 - 48 "b"^2)/(9"a"^2) = (16"b"^2)/(9"a"^2)`

x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`

x = `(-(8"b")/(3"a") +- sqrt ((16"b"^2)/(9"a"^2)))/2`

x = `(-(8"b")/(3"a") + (4"b")/(3"a")) / 2`  , x = `(-(8"b")/(3"a") - (4"b")/(3"a")) / 2`

x = `(-4"b")/(6"a")` , x = `(- 12"b")/(6"a")`

x = ` - (2"b")/(3"a")`  , x =` - (2"b")/"a"`