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Question
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
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Solution
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"`
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