Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
$2 x^{2}+x+4=0$
We have been given that,
$2 x^{2}+x+4=0$
Now divide throughout by 2. We get,
$x^{2}+\frac{1}{2} x+2=0$
Now take the constant term to the RHS and we get
$x^{2}+\frac{1}{2} x=-2$
Now add square of half of co-efficient of ‘x’ on both the sides. We have,
$x^{2}+\frac{1}{2} x+\left(\frac{1}{4}\right)^{2}=\left(\frac{1}{4}\right)^{2}-2$
$x^{2}+\left(\frac{1}{4}\right)^{2}+2\left(\frac{1}{4}\right) x=\frac{-31}{16}$
$\left(x+\frac{1}{4}\right)^{2}=-\frac{31}{16}$
Since RHS is a negative number, therefore the roots of the equation do not exist as the square of a number cannot be negative.
Therefore the roots of the equation do not exist.
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