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Question
Solve the following quadratic equation using formula method only
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
Solution
`5/4 "x"^2 - 2 sqrt 5 "x" + 4 = 0`
`5"x"^2 - 8 sqrt 5 "x" + 16 = 0`
a = 5 ; b = `- 8 sqrt 5` ; c = 16
D = b2 - 4ac
`= (- 8 sqrt 5)^2 - 4 (5)(15)`
= 40 - 300
= -260
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-(- 8 sqrt 5) +- sqrt -260)/(2 xx 5)`
x = `(8 sqrt 5 +- sqrt -260)/(2 xx 5)`
x = `(4 sqrt 5)/5` (Since `sqrt- 260` is not possible)
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