Relations and Functions

Relations and Functions

Question

solve each of the following equations:

space space space space space space square root of 2 space straight x squared space plus space straight x space plus space square root of 2 space equals space 0

Answer

Here,      space space space space space space space space space space straight D space equals space straight b 2 space minus space 4 ac space equals space left parenthesis 1 right parenthesis 2 space minus 4 space open parentheses square root of 2 close parentheses open parentheses square root of 2 close parentheses space equals space 1 space minus space 4 space straight x space 2 space equals space 1 space minus space 8 space equals space minus space 7 space less than space 0
Therefor, roots of given equation are imaginary and are given by
 space space space space space space space space space space space straight x space equals space fraction numerator negative straight b plus-or-minus square root of straight D over denominator 2 straight a end fraction space equals fraction numerator negative straight b space plus-or-minus square root of negative 7 end root over denominator 2 left parenthesis square root of 2 right parenthesis end root end fraction
i.e. "<pre

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