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Find the root of the following quadratic equations by the factorisation method: 32x2-5x-2 = 0 - Mathematics

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Sum

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

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

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Solution

Given equation is `3sqrt(2)x^2 - 5x - sqrt(2)` = 0

`3sqrt(2) x^2 - (6x - x) - sqrt(2)` = 0  ...[By splitting the middle term]

`3sqrt(2)x^2 - 6x + x - sqrt(2)` = 0

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

⇒ `3sqrt(2)x (x - sqrt(2)) + 1(x - sqrt(2))` = 0

⇒ `(x - sqrt(2))(3sqrt(2)x + 1)` = 0

Now `x - sqrt(2) = 0`

⇒ `x = sqrt(2)`

And `3sqrt(2)x + 1 = 0`

⇒ `x = -1/(3sqrt(2)) = (-sqrt(2))/6`

Hence the roots of the equation `3sqrt(2)x^2 - 5x - sqrt(2)` = 0 are `- sqrt(2)/6` and `sqrt(2)`.

Concept: Solutions of Quadratic Equations by Factorization
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.3 | Q 2.(iii) | Page 40
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