InterviewSolution
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InterviewSolution
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Factorize `(i) x^2+5sqrt(3)x +12` `(ii) x^2+3sqrt(3)x-30` |
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Answer» (i) The given expression is `x^2+5sqrt(3)x+12`. We split `5sqrt(3)` into two parts whose sum is `5sqrt(3)` and product 12. Clearly, `(4sqrt(3)+sqrt(3))=5sqrt(3) and (4sqrt(3)xx sqrt(3))=12`. `therefore x^2+5sqrt(3)x+12=x^2+4sqrt(3)x+sqrt(3)x +12` `=x(x+4sqrt(3))+sqrt(3)(x+4sqrt(3))` `=(x+4sqrt(3))(x+sqrt(3))` Hence, `x^2+5sqrt(3)x+12 =(x+4sqrt(3))(x+sqrt(3))`. (ii) The given expression is `x^2+3sqrt(3)x-30`. We split `3sqrt(3)` into two whose sum is `3sqrt(3)` and product `-30`. Clearly, `(5sqrt(3)-2sqrt(3))=3sqrt(3) and 5sqrt(3)xx {-2sqrt(3)}=-30`. `therefore x^2+3sqrt(3)x-30=x^2+5sqrt(3)x-2sqrt(3)x-30` `=x(x+5sqrt(3))-2sqrt(3)(x+5sqrt(3))` `=(x+5sqrt(3))(x-2sqrt(3))`. Hence, `x^2+3sqrt(3)x-30 =(x+5sqrt(3))(x-2sqrt(3))`. |
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