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

Sum

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

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

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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