Relations and Functions

Relations and Functions

Question

solve each of the following equations:

2x2 + x + 1 = 0

Answer

Here,        D = b2 - 4ac = (1)2 - 4 (2) (1) = 1 - 8 = -7 < 0
Therefore, roots of given equation are imaginary and are given  by

   space space space space space space space space space space space space space space straight x space equals space fraction numerator negative space straight b space plus-or-minus space square root of straight D over denominator 2 straight a end fraction space equals space fraction numerator negative 1 plus-or-minus square root of negative 7 end root over denominator 2 left parenthesis 2 right parenthesis end fraction

i.e.    space space space space space straight x space equals space fraction numerator negative 1 space plus space square root of 7 space straight i end root over denominator 4 end fraction comma space fraction numerator negative 1 space minus square root of 7 space straight i end root over denominator 4 end fraction

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