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प्रश्न
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
उत्तर
Given equation is `3x^2 + 5sqrt(5)x - 10` = 0
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 2sqrt(5) * sqrt(5)` = 0 ....[By splitting the middle term]
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 10` = 0
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 2sqrt(5) * sqrt(5)` = 0
⇒ `3x(x + 2sqrt(5)) - sqrt(5) (x + 2sqrt(5))` = 0
⇒ `(x + 2sqrt(5))(3x - sqrt(5))` = 0
Now, `x + 2sqrt(5)` = 0
⇒ x = `- 2sqrt(5)` and `3x - sqrt(5)` = 0
⇒ x = `sqrt(5)/3`
Hence, the roots of the equation `3x^2 + 5sqrt(5)x - 10` = 0 are `-2sqrt(5)` and `sqrt(5)/3`.
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