InterviewSolution
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InterviewSolution
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Solve the equation:`sqrt(3)x^2-sqrt(2)x+3sqrt(3)= 0` |
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Answer» The given equation is `sqrt(3)x^(2)-sqrt(2)x +3 sqrt(3) = 0` This is of the form `ax^(2) + bx + c = 0`, where `a = sqrt(3), b = -sqrt(2) and c = 3 sqrt(3)`. `therefore" "(b^(2)-4ac)={(-sqrt(2))^(2)-4 xx sqrt(3) xx 3 sqrt(3)}=(2-36)=-34 lt 0`. So, the given equation has complex roots. These roots are given by `(-b +- sqrt(b^(2)-4ac))/(2a)=(sqrt(2)+- sqrt(-34))/(2 xx sqrt(3))" "[because b^(2)-4ac=-34]` `=(sqrt(2)+-i sqrt(34))/(2 sqrt(3))` `therefore" ""solution set"={(sqrt(2)+i sqrt(34))/(2 sqrt(3)),(sqrt(2)-i sqrt(34))/(2 sqrt(3))}={(1)/(sqrt(6))+(sqrt(34))/(2 sqrt(3))i,(1)/(sqrt(6))-(sqrt(34))/(2 sqrt(3))i}`. |
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