Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(iv) $2x^2+x+4=0$

Answer 1

(iv) $2x^2+x+4=0$
$\Rightarrow 2x^2+x=-4$
On dividing both sides of the equation, we get
$\Rightarrow x^2+\frac{1}{2}x=-2$
$\Rightarrow x^2+2\times x\times \frac{1}{4}=-2$
On adding $(\frac{1}{4}{)}^2$ to both sides of the equation, we get
$\Rightarrow (x{)}^2+2\times x\times \frac{1}{4}+(\frac{1}{4}{)}^2=(\frac{1}{4}{)}^2-2\Rightarrow (x+\frac{1}{4}{)}^2=\frac{1}{16}-2\Rightarrow (x+\frac{1}{4}{)}^2=-\frac{31}{16}$
However, the square of number cannot be negative.
Therefore, there is no real root for the given equation.