Find the roots of the following quadratic equations by the factorisation method.
`3sqrt(2)x^(2)-5x-sqrt(2)=0`

Explanation

Give 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`
`implies 3sqrt(2)x(x-sqrt(2))+1(x-sqrt(2))=0`
`implies (x-sqrt(2)(3sqrt(2)x+1)=0`
Now, `x-sqrt(2)=0impliesx=sqrt(2)`
and `3sqrt(2)x+1=0`
`implies 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)`.