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Question
Solve the following equation by using formula:
2x2 – 6x + 3 = 0
Solution
2x2 – 6x + 3 = 0
Here a = 2, b = -6, c = 3
then D = b2 - 4ac
= (-6)2 - 4 x 2 x 3
= 36 - 24
= 12
Now
x = `(-b ± sqrt("D"))/(2a)`
= `((-6) ± sqrt(12))/(2 xx 2)`
= `(6 ±2sqrt(3))/(4)`
∴ x1 = `(6 + 2sqrt(3))/(4)`
= `(2(3 + sqrt(3)))/(4)`
= `(3 + sqrt(3))/(2)`
x2 = `(6 - 2sqrt(3))/(4)`
= `(2(3 - sqrt(3)))/(4)`
= `(3 - sqrt(3))/(2)`
Hence x = `(3 + sqrt(3))/(2), (3 - sqrt(3))/(2)`.
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