Sum

Find the root of the following quadratic equations by the factorisation method:

`3x^2 + 5sqrt(5) - 10` = 0

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#### Solution

Given equation is `3x^2 + 5sqrt(5) - 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`

Concept: Solutions of Quadratic Equations by Factorization

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