InterviewSolution
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InterviewSolution
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Solve the equation:`sqrt(2)x^2+x+sqrt(2)=0` |
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Answer» The given equation is `sqrt(2)x^(2) + x + sqrt(2) = 0`. This is of the form `ax^(2)+bx+c=0`, where `a = sqrt(2), b = 1 and c = sqrt(2)`. `therefore" "(b^(2)-4ac)=(1^(2)-4xx sqrt(2)xx sqrt(2))=(1-8) =-7 lt 0`. So, the given equation has complex roots. These roots are given by `(-b +- sqrt(b^(2)-4ac))/(2a)=(-1 +- sqrt(-7))/(2 sqrt(2))" "[because b^(2)-4ac = -7]` `=(-1 +- i sqrt(7))/(2 sqrt(2))`. `therefore" ""solution set"={(-1+i sqrt(7))/(2 sqrt(2)),(-1-i sqrt(7))/(2 sqrt(2))}={(-1)/(2 sqrt(2))+(sqrt(7))/(2 sqrt(2))i,(-1)/(2 sqrt(2))-(sqrt(7))/(2 sqrt(2))i}`. |
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