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प्रश्न
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Determine the nature of the roots of the following quadratic equation:
`3x^2 - 4sqrt3x + 4 = 0`
उत्तर
`3x^2 - 4sqrt3x + 4 = 0`
Comparing it with ax2 + bx + c = 0, we get
a = 3, b = `-4sqrt3` and c = 4
Discriminant = b2 - 4ac
= `(-4sqrt3)^2 - 4(3)(4)`
= 48 - 48
= 0
As b2 - 4ac = 0,
Therefore, real roots exist for the given equation and they are equal to each other.
And the roots will be `(-b)/(2a) `
i.e, `(-(-4)sqrt3)/(2xx3) and (-(-4sqrt3))/(2xx3)`
= `(4sqrt3)/(2sqrt3 xx sqrt3) and (4sqrt3)/(2sqrt3 xxsqrt3)`
Therefore, the roots are `2/sqrt3 and 2/sqrt3.`
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