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प्रश्न
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
उत्तर
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0
Comparing the above equation with ax2 + bx + c = 0, we get
a = `sqrt(3)`, b = `sqrt(2)`, c = `-2sqrt(3)`
∴ b2 – 4ac = `(sqrt(2))^2 - 4 xx sqrt(3) xx (-2sqrt(3))`
= 2 + 24
= 26
x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`
= `(-sqrt(2) +- sqrt(26))/(2sqrt(3))`
= `(sqrt(2)(-1 +- sqrt(13)))/(2sqrt(3))`
= `(sqrt(2)(-1 +- sqrt(13)))/(2sqrt(3)) xx sqrt(2)/(sqrt(2)`
= `(2(-1 +- sqrt(13)))/(2sqrt(6))`
∴ x = `(-1 +- sqrt(13))/sqrt(6)`
∴ x = `(-1 + sqrt(13))/sqrt(6)` or x = `(-1 - sqrt(13))/sqrt(6)`
∴ The roots of the given equation are `(-1 + sqrt(13))/sqrt(6)` and x = `(-1 - sqrt(13))/sqrt(6)`.
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