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Factorise sqrt(3)x^(2)+10x+3sqrt(3)...

Factorise `sqrt(3)x^(2)+10x+3sqrt(3)`

A

`(x+3sqrt(3))(sqrt(3)x-1)`

B

`(x-3sqrt(3))(sqrt(3)x-1)`

C

`(x+3sqrt(3))(sqrt(3)x+1)`

D

`(x-3sqrt(3))(sqrt(3)x+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `a=sqrt(3),b=10,c=3sqrt(3)`
`therefore a xx c = sqrt(3)xx3sqrt(3)=9`
Now, we take two factors of 9 whose sum is 10.
Such factors are 9 and 1.
`therefore sqrt(3)x^(2)+10x+3sqrt(3)=sqrt(3)x^(2)+(9+1)x+3sqrt(3)=sqrt(3)x^(2)+9x+x+3sqrt(3)`
`=sqrt(3)x(x+3sqrt(3))+1(x+3sqrt(3))=(x+3sqrt(3))(sqrt(3)x+1)`
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