Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$2 x^{2} + x + 4 = 0$

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Solution

$equals 2 x squared plus x plus 4 equals 0 equals x squared plus x over 2 plus 2 equals 0 equals x squared plus 2 left parenthesis 1 fourth right parenthesis x plus left parenthesis 1 fourth right parenthesis squared minus left parenthesis 1 fourth right parenthesis squared plus 2 equals 0 equals left parenthesis x plus 1 fourth right parenthesis squared equals left parenthesis 1 fourth right parenthesis squared minus 2 equals left parenthesis x plus 1 fourth right parenthesis squared equals 1 over 16 minus 2 equals left parenthesis x plus 1 fourth right parenthesis squared equals fraction numerator negative 31 over denominator 16 end fraction$
Here, Square is equal to negative value. Hence real roots don't exist

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Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$4 x^{2} + 4 \sqrt{3} x + 3 = 0$

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.

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2 x^{2} + x + 4 = 0

2 x^{2} - 7 x + 3 = 0

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4 x^{2} + 4 \sqrt{3} x + 3 = 0

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